Статті в журналах: "Lie triple system"

1

Okubo, Susumu, and Noriaki Kamiya. "Jordan–Lie Super Algebra and Jordan–Lie Triple System." Journal of Algebra 198, no. 2 (December 1997): 388–411. http://dx.doi.org/10.1006/jabr.1997.7144.

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2

DONG, YAN-QIN, QING-CHENG ZHANG, and YONG-ZHENG ZHANG. "RESTRICTED AND QUASI-TORAL RESTRICTED LIE TRIPLE SYSTEMS." Journal of Algebra and Its Applications 11, no. 05 (September 26, 2012): 1250093. http://dx.doi.org/10.1142/s0219498812500934.

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In this paper, we first discuss the nilpotency of restricted Lie triple systems and the condition of existence of p-mappings on Lie triple systems. Second, we devote our attention to prove the uniqueness of the decomposition as a direct sum of p-ideals of a restricted Lie triple system. Finally, we study how a quasi-toral restricted Lie triple system T with zero center and of minimal dimension should be.

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3

Cao, Yan, Jian Zhang, and Yunan Cui. "On split Lie color triple systems." Open Mathematics 17, no. 1 (April 9, 2019): 267–81. http://dx.doi.org/10.1515/math-2019-0023.

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Abstract In order to begin an approach to the structure of arbitrary Lie color triple systems, (with no restrictions neither on the dimension nor on the base field), we introduce the class of split Lie color triple systems as the natural generalization of split Lie triple systems. By developing techniques of connections of roots for this kind of triple systems, we show that any of such Lie color triple systems T with a symmetric root system is of the form T = U + ∑[α]∈Λ1/∼ I[α] with U a subspace of T0 and any I[α] a well described (graded) ideal of T, satisfying {I[α], T, I[β]} = 0 if [α] ≠ [β]. Under certain conditions, in the case of T being of maximal length, the simplicity of the triple system is characterized.

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4

Xiao, Yunpeng, Wen Teng, and Fengshan Long. "Generalized Reynolds Operators on Hom-Lie Triple Systems." Symmetry 16, no. 3 (February 21, 2024): 262. http://dx.doi.org/10.3390/sym16030262.

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In this paper, we first introduce the notion of generalized Reynolds operators on Hom-Lie triple systems associated to a representation and a 3-cocycle. Then, we develop a cohomology of generalized Reynolds operators on Hom-Lie triple systems. As applications, we use the first cohomology group to classify linear deformations and we study the obstruction class of an extendable order n deformation. Finally, we introduce and investigate Hom-NS-Lie triple system as the underlying structure of generalized Reynolds operators on Hom-Lie triple systems.

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5

Zhou, Jia, Liangyun Chen, and Yao Ma. "Generalized derivations of Lie triple systems." Open Mathematics 14, no. 1 (January 1, 2016): 260–71. http://dx.doi.org/10.1515/math-2016-0024.

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AbstractIn this paper, we present some basic properties concerning the derivation algebra Der (T), the quasiderivation algebra QDer (T) and the generalized derivation algebra GDer (T) of a Lie triple system T, with the relationship Der (T) ⊆ QDer (T) ⊆ GDer (T) ⊆ End (T). Furthermore, we completely determine those Lie triple systems T with condition QDer (T) = End (T). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.

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6

KAMIYA, NORIAKI, DANIEL MONDOC, and SUSUMU OKUBO. "A STRUCTURE THEORY OF (−1,−1)-FREUDENTHAL KANTOR TRIPLE SYSTEMS." Bulletin of the Australian Mathematical Society 81, no. 1 (October 2, 2009): 132–55. http://dx.doi.org/10.1017/s0004972709000732.

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AbstractIn this paper we discuss the simplicity criteria of (−1,−1)-Freudenthal Kantor triple systems and give examples of such triple systems, from which we can construct some Lie superalgebras. We also show that we can associate a Jordan triple system to any (ε,δ)-Freudenthal Kantor triple system. Further, we introduce the notion of δ-structurable algebras and connect them to (−1,δ)-Freudenthal Kantor triple systems and the corresponding Lie (super)algebra construction.

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7

Kamiya, Noriaki, та Susumu Okubo. "Symmetry of Lie algebras associated with (ε, δ)-Freudenthal-Kantor triple system". Proceedings of the Edinburgh Mathematical Society 59, № 1 (13 липня 2015): 169–92. http://dx.doi.org/10.1017/s0013091514000406.

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AbstractSymmetry groups of Lie algebras and superalgebras constructed from (∈, δ)-Freudenthal-Kantor triple systems have been studied. In particular, for a special (ε, ε)-Freudenthal–Kantor triple, it is the SL(2) group. Also, the relationship between two constructions of Lie algebras from structurable algebras has been investigated.

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8

Xia, Haobo. "3-Derivations and 3-Automorphisms on Lie Algebras." Mathematics 10, no. 5 (February 28, 2022): 782. http://dx.doi.org/10.3390/math10050782.

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In this paper, first we establish the explicit relation between 3-derivations and 3- automorphisms of a Lie algebra using the differential and exponential map. More precisely, we show that the Lie algebra of 3-derivations is the Lie algebra of the Lie group of 3-automorphisms. Then we study the derivations and automorphisms of the standard embedding Lie algebra of a Lie triple system. We prove that derivations and automorphisms of a Lie triple system give rise to derivations and automorphisms of the corresponding standard embedding Lie algebra. Finally we compute the 3-derivations and 3-automorphisms of 3-dimensional real Lie algebras.

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9

Zhang, Zhixue, Liangyun Chen, Wenli Liu, and Ximei Bai. "The Frattini Subsystem of a Lie Triple System." Communications in Algebra 37, no. 10 (October 9, 2009): 3750–59. http://dx.doi.org/10.1080/00927870802502936.

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10

Ma, Lili, and Qiang Li. "Cohomology and its applications on multiplicative Hom-$ \delta $-Jordan Lie color triple systems." AIMS Mathematics 9, no. 9 (2024): 25936–55. http://dx.doi.org/10.3934/math.20241267.

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The theory of cohomologies on multiplicative Hom-$ \delta $-Jordan Lie color triple systems is given. As an application, deformations and extensions on the multiplicative Hom-$ \delta $-Jordan Lie color triple system are characterized in view of relevant cohomology.

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11

Wang, Yongjie, Yiqian Shi, and Yun Gao. "The Steinberg Lie Algebra st2(S)." Algebra Colloquium 23, no. 01 (January 6, 2016): 129–36. http://dx.doi.org/10.1142/s100538671600016x.

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12

Fontanals, Cristina Draper. "Homogeneous Einstein manifolds based on symplectic triple systems." Communications in Mathematics 28, no. 2 (September 1, 2020): 139–54. http://dx.doi.org/10.2478/cm-2020-0016.

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AbstractFor each simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous manifold. It is proved that this is an Einstein manifold.

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13

Elduque, Alberto, and Susumu Okubo. "Special Freudenthal–Kantor triple systems and Lie algebras with dicyclic symmetry." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 6 (November 15, 2011): 1225–62. http://dx.doi.org/10.1017/s0308210510000569.

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We study Lie algebras endowed with an action by automorphisms of the dicyclic group of degree 3. The close connections of these algebras with Lie algebras graded over the non-reduced root system BC1, with J-ternary algebras and with Freudenthal–Kantor triple systems are explored.

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14

Wu, Xueru, Liangyun Chen, and Yao Ma. "Derivation extensions on Leibniz triple systems." Filomat 37, no. 23 (2023): 7905–18. http://dx.doi.org/10.2298/fil2323905w.

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In this paper, we first define a concrete representation on an abelian extension of a Leibniz triple system L by a Leibniz triple system A. Using this new representation we construct the third-order cohomology classes by derivations of A and L, which characterize the splitting property of above abelian extensions. Then we study the obstruction for extensibility of derivation pairs. We prove that the set of compatible derivation pairs can define a Lie algebra, whose representation can also characterize the extensibility of the compatible derivation pairs.

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15

Mykytyuk, I. V. "The Lie triple system of the symmetric space $F_4 / Spin(9)$." Asian Journal of Mathematics 6, no. 4 (2002): 713–18. http://dx.doi.org/10.4310/ajm.2002.v6.n4.a6.

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16

Chen, Liang Yun, and Dong Liu. "The Frattini p-subsystem of a solvable restricted Lie triple system." Acta Mathematica Sinica, English Series 26, no. 10 (September 15, 2010): 1887–98. http://dx.doi.org/10.1007/s10114-010-9251-8.

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17

Attan, Sylvain, and A. Nourou Issa. "Hom-Lie Triple System and Hom-Bol Algebra Structures on Hom-Maltsev and Right Hom-Alternative Algebras." International Journal of Mathematics and Mathematical Sciences 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/4528685.

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Every multiplicative Hom-Maltsev algebra has a natural multiplicative Hom-Lie triple system structure. Moreover, there is a natural Hom-Bol algebra structure on every multiplicative Hom-Maltsev algebra and on every multiplicative right (or left) Hom-alternative algebra.

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18

Palmkvist, Jakob. "A realization of the Lie algebra associated to a Kantor triple system." Journal of Mathematical Physics 47, no. 2 (February 2006): 023505. http://dx.doi.org/10.1063/1.2168690.

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19

Autenried, Christian, Kenro Furutani, Irina Markina, and Alexander Vasiľev. "Pseudo-metric 2-step nilpotent Lie algebras." Advances in Geometry 18, no. 2 (April 25, 2018): 237–63. http://dx.doi.org/10.1515/advgeom-2017-0051.

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Abstract The metric approach to studying 2-step nilpotent Lie algebras by making use of non-degenerate scalar products is realised. We show that a 2-step nilpotent Lie algebra is isomorphic to its standard pseudo-metric form, that is a 2-step nilpotent Lie algebra endowed with some standard non-degenerate scalar product compatible with the Lie bracket. This choice of the standard pseudo-metric form allows us to study the isomorphism properties. If the elements of the centre of the standard pseudo-metric form constitute a Lie triple system of the pseudo-orthogonal Lie algebra, then the original 2-step nilpotent Lie algebra admits integer structure constants. Among particular applications we prove that pseudo H-type algebras have bases with rational structure constants, which implies that the corresponding pseudo H-type groups admit lattices.

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20

Chen, Liangyun, Dong Liu, and Xiaoning Xu. "Some subsystems of a lie triple system closely related to its Frattini subsystem." Chinese Annals of Mathematics, Series B 34, no. 5 (July 19, 2013): 791–800. http://dx.doi.org/10.1007/s11401-013-0786-8.

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21

Webb, G. M., M. Brio, and G. P. Zank. "Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves." Journal of Plasma Physics 54, no. 2 (October 1995): 201–44. http://dx.doi.org/10.1017/s0022377800018456.

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Lie symmetries, conservation laws, and Lagrangian and Hamiltonian formulations of the triple degenerate, derivative nonlinear Schrödinger (TDNLS) equations for weakly nonlinear dispersive, magnetohydrodynamic (MHD) waves are derived. The equations describe how Alfvén waves propagating parallel to the background magnetic field B interact with the magneto-acoustic modes near the triple umbilic point where the fast, slow and Alfvén mode phase speeds coincide. The Lie point symmetries are used to derive classical similarity solutions of the equations. In particular, the similarity solutions corresponding to time translation, space translation and rotational invariance symmetries are reduced to quadrature. The dispersionless TDNLS system is of hydrodynamic type, and has three families of characteristics analogous to the slow, intermediate and fast modes of MilD. The Riemann invariants corresponding to each of these families are obtained in closed analytic form. Examples of solitary wave and periodic travelling wave solutions are investigated by plotting the contours of the Hamiltonian H(v, w) in the (v, w) phase plane, where the canonical variables v and w correspond to the normalized transverse magnetic field perturbations. An analysis of the prolongation Lie algebra is carried out in order to investigate the integrability of the equations.

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22

Kamiya, Noriaki, and Susumu Okubo. "A construction of simple Jordan superalgebra of F type from a Jordan–Lie triple system." Annali di Matematica Pura ed Applicata 181, no. 3 (August 2002): 339–48. http://dx.doi.org/10.1007/s102310100045.

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23

Sbitneva, L. "Differential equations of smooth loops related to some space-time models: Integrability conditions and geometry." Journal of Knot Theory and Its Ramifications 27, no. 07 (June 2018): 1841004. http://dx.doi.org/10.1142/s0218216518410043.

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The original approach of Lie to the theory of transformation groups acting on smooth manifolds, on the basis of differential equations, being applied to smooth loops, has permitted the development of the infinitesimal theory of smooth loops generalizing the Lie group theory. A loop with the law of associativity verified for its binary operation is a group. It has been shown that the system of differential equations characterizing a smooth loop with the right Bol identity and the integrability conditions lead to the binary-ternary algebra as a proper infinitesimal object, which turns out to be the Bol algebra (i.e. a Lie triple system with an additional bilinear skew-symmetric operation). There exist the analogous considerations for Moufang loops. We will consider the differential equations of smooth loops, generalizing smooth left Bol loops, with the identities that are the characteristic identities for the algebraic description of some relativistic space-time models. Further examinations of the integrability conditions for the differential equations allow us to introduce the proper infinitesimal object for some subclass of loops under consideration. The geometry of corresponding homogeneous spaces can be described in terms of tensors of curvature and torsion.

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24

Chtioui, T., S. Mabrouk, and A. Makhlouf. "Hom–Jordan–Malcev–Poisson algebras." Ukrains’kyi Matematychnyi Zhurnal 74, no. 11 (December 26, 2022): 1571–82. http://dx.doi.org/10.37863/umzh.v74i11.6360.

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UDC 512.5 We provide and study a Hom-type generalization of Jordan–Malcev–Poisson algebras called Hom–Jordan–Malcev–Poisson algebras. We show that they are closed under twisting by suitable self-maps and give a characterization of admissible Hom–Jordan–Malcev–Poisson algebras. In addition, we introduce the notion of pseudo-Euclidian Hom–Jordan–Malcev–Poisson algebras and describe its T * -extension. Finally, we generalize the notion of Lie–Jordan–Poisson triple system to the Hom setting and establish its relationships with Hom–Jordan–Malcev–Poisson algebras.

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25

Neukirch, Sébastien, Arnaud Antkowiak, and Jean-Jacques Marigo. "The bending of an elastic beam by a liquid drop: a variational approach." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2157 (September 8, 2013): 20130066. http://dx.doi.org/10.1098/rspa.2013.0066.

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We study the interaction of a liquid drop with an elastic beam in the case where bending effects dominate. We use a variational approach to derive equilibrium equations for the system in the presence of gravity and in the presence or absence of contact line pinning. We show that the derived equilibrium equations for the beam subsystem reveal the external forces applied on the beam by the liquid and vapour phases. Among these, the force applied at the triple line (the curve where the three phases meet) is found to lie along the liquid–vapour interface.

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26

Marquis, Robert, and P. Stephen Kumarapeli. "An Early Cambrian deltaic–fluvial model for an Iapetan rift-arm drainage system, southeastern Quebec." Canadian Journal of Earth Sciences 30, no. 6 (June 1, 1993): 1254–61. http://dx.doi.org/10.1139/e93-107.

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Based on the model that during the rifting stage beginning at ca. 590 Ma, the Ottawa Graben, an Iapetan failed arm, localized a large river that flowed into the nascent Iapetus, a search was made for the related fluvial and deltaic deposits. The search led to the identification of fluvial deposits as predicted by the model. Deltaic deposits were also identified despite complications brought about by deformation, metamorphism, and thrusting, although they probably belong to a late phase of delta buildup in the Early Cambrian. Older deltaic deposits of the river probably lie buried beneath a volcanic shield that built up at the proximal end of the graben ca. 554 Ma. The successful application of the model supports the paradigm of rift-arm – failed-arm rivers and their deltas as proposed by K. Burke and J.F. Dewey nearly two decades ago. Investigations based on this paradigm, in appropriate geological situations, may provide insights into problems related to continental rifting and breakup and provide information for the reconstruction of ancient rift–rift–rift (rrr) triple junctions and plate boundaries.

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27

Alvarez, Gabriella E., Scott W. Randall, Yuanyuan Su, Arnab Sarkar, Stephen Walker, Nicholas P. Lee, Craig L. Sarazin, and Elizabeth Blanton. "Suzaku Observations of the Cluster Outskirts and Intercluster Filament in the Triple Merger Cluster A98." Astrophysical Journal 938, no. 1 (October 1, 2022): 51. http://dx.doi.org/10.3847/1538-4357/ac91d3.

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Abstract We present Suzaku observations of the Abell 98 (A98) triple galaxy cluster system and the purported intercluster filament. The three subclusters are expected to lie along a large-scale cosmic filament. With partial azimuthal coverage of the northernmost cluster, we find that the inferred entropy profile of this relatively low-mass cluster (kT ≈ 2.8 keV) adheres to expectations from models of self-similar pure gravitational collapse in the region of the virial radius. There is evidence of extended structure beyond r 200 to the north of the northernmost cluster, along the merger axis, with properties consistent that are expected for the warm–hot intergalactic medium ( kT = 0.11 − 0.02 + 0.01 keV and n e = 7.6 × 10−5 ± 3.6 × 10−5 cm−3). No such emission is detected at the same radius in regions away from the merger axis, consistent with the expectation that the merger axis of this triple system lies along a large-scale cosmic filament. In the bridge region between A98N and A98S, there is evidence of filamentary emission at the 2.2σ level, as well as a tentative detection of cool gas (kT ∼ 1 keV). The entropy profile of this intercluster filament suggests that the A98 system is most likely aligned closer to the plane of the sky rather than along the line of sight. The structure to the north of the system, as well as in-between A98N and A98S, is indicative that the clusters are connected to a larger-scale structure spanning at least 4 Mpc.

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28

Hall, B. G., P. W. Betts, and J. C. Wootton. "DNA sequence analysis of artificially evolved ebg enzyme and ebg repressor genes." Genetics 123, no. 4 (December 1, 1989): 635–48. http://dx.doi.org/10.1093/genetics/123.4.635.

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Abstract The ebg system has been used as a model to study the artificial selection of new catalytic functions of enzymes and of inducer specificities of repressors. A series of mutant enzymes with altered catalytic specificities were previously characterized biochemically as were the changes in inducer specificities of mutant, but fully functional, repressors. The wild type ebg operon has been sequenced, and the sequence differences of the mutant enzymes and repressors have been determined. We now report that, contrary to our previous understanding, ebg enzyme contains 180-kD alpha-subunits and 20-kD beta-subunits, both of which are required for full activity. Mutations that dramatically affect substrate specificity and catalytic efficiency lie in two distinct regions, both well outside of the active site region. Mutations that affect inducer specificity of the ebg repressor lie within predicted sugar binding domains. Comparisons of the ebg beta-galactosidase and repressor with homologous proteins of the Escherichia coli and Klebsiella pneumoniae lac operons, and with the galactose operon repressor, suggest that the ebg and lac operons diverged prior to the divergence of E. coli from Klebsiella. One case of a triple substitution as the consequence of a single event is reported, and the implications of that observation for mechanisms of spontaneous mutagenesis are discussed.

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29

Lohe, M. A. "Higher-order synchronization on the sphere." Journal of Physics: Complexity 3, no. 1 (December 29, 2021): 015003. http://dx.doi.org/10.1088/2632-072x/ac42e1.

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Abstract We construct a system of N interacting particles on the unit sphere S d − 1 in d-dimensional space, which has d-body interactions only. The equations have a gradient formulation derived from a rotationally-invariant potential of a determinantal form summed over all nodes, with antisymmetric coefficients. For d = 3, for example, all trajectories lie on the two-sphere and the potential is constructed from the triple scalar product summed over all oriented two-simplices. We investigate the cases d = 3, 4, 5 in detail, and find that the system synchronizes from generic initial values for both positive and negative coupling coefficients, to a static final configuration in which the particles lie equally spaced on S d − 1 . Completely synchronized configurations also exist, but are unstable under the d-body interactions. We compare the relative effect of two-body and d-body forces by adding the well-studied two-body interactions to the potential, and find that higher-order interactions enhance the synchronization of the system, specifically, synchronization to a final configuration consisting of equally spaced particles occurs for all d-body and two-body coupling constants of any sign, unless the attractive two-body forces are sufficiently strong relative to the d-body forces. In this case the system completely synchronizes as the two-body coupling constant increases through a positive critical value, with either a continuous transition for d = 3, or discontinuously for d = 5. Synchronization also occurs if the nodes have distributed natural frequencies of oscillation, provided that the frequencies are not too large in amplitude, even in the presence of repulsive two-body interactions which by themselves would result in asynchronous behaviour.

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30

Hodge, Terrell L. "Lie Triple Systems, Restricted Lie Triple Systems, and Algebraic Groups." Journal of Algebra 244, no. 2 (October 2001): 533–80. http://dx.doi.org/10.1006/jabr.2001.8890.

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31

Kluge, Zachery A., Kevin J. Shinners, and Matthew F. Digman. "Performance of a Towed Implement with Electrically Driven Traction-Assist System." Applied Engineering in Agriculture 41, no. 2 (2025): 137–43. https://doi.org/10.13031/aea.16285.

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HighlightsAn electrically driven traction-assist powered axle was integrated into a triple-axle large-capacity slurry tanker.The traction-assist system reduced tractor drawbar pull, wheel slip, and drawbar power requirements.Specific fuel consumption showed no significant reduction with the implementation of the traction-assist system.Abstract. Hybrid diesel engine-generator systems represent a near-term application that precedes the widespread adoption of fully electric tractors. One such application is a traction-assist system on one or more of the axles of a towed implement. Given the scarcity of published evaluations on such applications, we investigated the effectiveness of this system on a large slurry tanker. The investigation involved testing a 36 m3 tanker with partial and full loads (42.4 and 52.9 Mg) in conditions where traction was favorable, and field slopes were minimal. A randomized and replicated experiment was conducted involving two variables: tanker load (either full or partially full) and traction-assist (engaged or disengaged), resulting in a two-by-two design. The results indicated significant reductions in tractor drawbar pull, wheel slip, and drawbar power requirements occurred with the traction-assist system engaged. However, despite these encouraging results, no significant decrease was observed in specific fuel consumption. The favorable traction conditions might have limited the effectiveness of the traction-assist system in reducing energy consumption. The positive traction and wheel slip results suggest that the system’s greatest potential may lie in soft, wet soil environments and steep terrain. In such challenging scenarios, the traction-assist system will likely demonstrate its full utility by enhancing traction, minimizing tractor wheel slip, and ultimately boosting productivity. Future research should be conducted under these more challenging conditions. Keywords: Electric drive, Slurry, Tanker, Traction, Tractor.

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32

Flint, Mike, Laura K. McMullan, Kimberly A. Dodd, Brian H. Bird, Marina L. Khristova, Stuart T. Nichol, and Christina F. Spiropoulou. "Inhibitors of the Tick-Borne, Hemorrhagic Fever-Associated Flaviviruses." Antimicrobial Agents and Chemotherapy 58, no. 6 (March 24, 2014): 3206–16. http://dx.doi.org/10.1128/aac.02393-14.

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ABSTRACTNo antiviral therapies are available for the tick-borne flaviviruses associated with hemorrhagic fevers: Kyasanur Forest disease virus (KFDV), both classical and the Alkhurma hemorrhagic fever virus (AHFV) subtype, and Omsk hemorrhagic fever virus (OHFV). We tested compounds reported to have antiviral activity against members of theFlaviviridaefamily for their ability to inhibit AHFV replication. 6-Azauridine (6-azaU), 2′-C-methylcytidine (2′-CMC), and interferon alpha 2a (IFN-α2a) inhibited the replication of AHFV and also KFDV, OHFV, and Powassan virus. The combination of IFN-α2a and 2′-CMC exerted an additive antiviral effect on AHFV, and the combination of IFN-α2a and 6-azaU was moderately synergistic. The combination of 2′-CMC and 6-azaU was complex, being strongly synergistic but with a moderate level of antagonism. The antiviral activity of 6-azaU was reduced by the addition of cytidine but not guanosine, suggesting that it acted by inhibiting pyrimidine biosynthesis. To investigate the mechanism of action of 2′-CMC, AHFV variants with reduced susceptibility to 2′-CMC were selected. We used a replicon system to assess the substitutions present in the selected AHFV population. A double NS5 mutant, S603T/C666S, and a triple mutant, S603T/C666S/M644V, were more resistant to 2′-CMC than the wild-type replicon. The S603T/C666S mutant had a reduced level of replication which was increased when M644V was also present, although the replication of this triple mutant was still below that of the wild type. The S603 and C666 residues were predicted to lie in the active site of the AHFV NS5 polymerase, implicating the catalytic center of the enzyme as the binding site for 2′-CMC.

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33

Rodríguez-Lobato, Luis Gerardo, Aina Oliver-Caldés, David F. Moreno, Carlos Fernández de Larrea, and Joan Bladé. "Why Immunotherapy Fails in Multiple Myeloma." Hemato 2, no. 1 (December 22, 2020): 1–42. http://dx.doi.org/10.3390/hemato2010001.

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Multiple myeloma remains an incurable disease despite great advances in its therapeutic landscape. Increasing evidence supports the belief that immune dysfunction plays an important role in the disease pathogenesis, progression, and drug resistance. Recent efforts have focused on harnessing the immune system to exert anti-myeloma effects with encouraging outcomes. First-in-class anti-CD38 monoclonal antibody, daratumumab, now forms part of standard treatment regimens in relapsed and refractory settings and is shifting to front-line treatments. However, a non-negligible number of patients will progress and be triple refractory from the first line of treatment. Antibody-drug conjugates, bispecific antibodies, and chimeric antigen receptors (CAR) are being developed in a heavily pretreated setting with outstanding results. Belantamab mafodotin-blmf has already received approval and other anti-B-cell maturation antigen (BCMA) therapies (CARs and bispecific antibodies are expected to be integrated in therapeutic options against myeloma soon. Nonetheless, immunotherapy faces different challenges in terms of efficacy and safety, and manufacturing and economic drawbacks associated with such a line of therapy pose additional obstacles to broadening its use. In this review, we described the most important clinical data on immunotherapeutic agents, delineated the limitations that lie in immunotherapy, and provided potential insights to overcome such issues.

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34

García, Esther, Miguel Gómez Lozano, and Erhard Neher. "Nondegeneracy for Lie Triple Systems and Kantor Pairs." Canadian Mathematical Bulletin 54, no. 3 (September 1, 2011): 442–55. http://dx.doi.org/10.4153/cmb-2011-023-9.

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AbstractWe study the transfer of nondegeneracy between Lie triple systems and their standard Lie algebra envelopes as well as between Kantor pairs, their associated Lie triple systems, and their Lie algebra envelopes. We also show that simple Kantor pairs and Lie triple systems in characteristic 0 are nondegenerate.

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35

Smirnov, O. N. "Imbedding of Lie triple systems into Lie algebras." Journal of Algebra 341, no. 1 (September 2011): 1–12. http://dx.doi.org/10.1016/j.jalgebra.2011.06.011.

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36

Calderón Martín, Antonio J. "On split Lie triple systems." Proceedings - Mathematical Sciences 119, no. 2 (April 2009): 165–77. http://dx.doi.org/10.1007/s12044-009-0017-0.

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37

Baklouti, Amir. "Quadratic Hom-Lie triple systems." Journal of Geometry and Physics 121 (November 2017): 166–75. http://dx.doi.org/10.1016/j.geomphys.2017.06.013.

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38

Ma, Lili, and Liangyun Chen. "On -Jordan Lie triple systems." Linear and Multilinear Algebra 65, no. 4 (June 26, 2016): 731–51. http://dx.doi.org/10.1080/03081087.2016.1202184.

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39

Hopkins, N. C. "Nilpotent Ideals in Lie and Anti-Lie Triple Systems." Journal of Algebra 178, no. 2 (December 1995): 480–92. http://dx.doi.org/10.1006/jabr.1995.1361.

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40

Ma, Yao, Liangyun Chen, and Jie Lin. "Systems of Quotients of Lie Triple Systems." Communications in Algebra 42, no. 8 (April 4, 2014): 3339–49. http://dx.doi.org/10.1080/00927872.2013.783040.

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41

Li, Qiang, and Lili Ma. "1-parameter formal deformations and abelian extensions of Lie color triple systems." Electronic Research Archive 30, no. 7 (2022): 2524–39. http://dx.doi.org/10.3934/era.2022129.

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<abstract>The purpose of this paper is to discuss Lie color triple systems. The cohomology theory of Lie color triple systems is established, then 1-parameter formal deformations and abelian extensions of Lie color triple systems are studied using cohomology.</abstract>

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42

Baklouti, Amir. "Hom-Lie triple systems with involution." New Trends in Mathematical Science 1, no. 7 (March 29, 2019): 90–101. http://dx.doi.org/10.20852/ntmsci.2019.346.

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43

Lin, Jie, Yan Wang, and Shaoqiang Deng. "T∗-extension of Lie triple systems." Linear Algebra and its Applications 431, no. 11 (November 2009): 2071–83. http://dx.doi.org/10.1016/j.laa.2009.07.001.

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44

Najati, Abbas. "Generalized Derivations on Lie Triple Systems." Results in Mathematics 54, no. 1-2 (October 30, 2008): 143–47. http://dx.doi.org/10.1007/s00025-008-0300-x.

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45

Calderón Martín, Antonio J., and M. Forero Piulestán. "On split Lie triple systems II." Proceedings - Mathematical Sciences 120, no. 2 (April 2010): 185–98. http://dx.doi.org/10.1007/s12044-010-0021-4.

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46

Hopkins, Nora C. "Forms of lie module triple systems." Communications in Algebra 15, no. 8 (January 1987): 1709–26. http://dx.doi.org/10.1080/00927878708823498.

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47

Hopkins, Nora C. "Simplicity of lie module triple systems." Communications in Algebra 19, no. 8 (January 1991): 2231–37. http://dx.doi.org/10.1080/00927879108824256.

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48

Calderón Martín, Antonio J. "On Simple Split Lie Triple Systems." Algebras and Representation Theory 12, no. 2-5 (March 4, 2009): 401–15. http://dx.doi.org/10.1007/s10468-009-9150-9.

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49

Yara, Hamdiatou, and Patricia L. Zoungrana. "ON RESTRICTED HOM-LIE TRIPLE SYSTEMS." Universal Journal of Mathematics and Mathematical Sciences 18 (January 5, 2023): 35–52. http://dx.doi.org/10.17654/2277141723003.

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50

Teng, Wen, Fengshan Long, and Yu Zhang. "Cohomologies of modified $ \lambda $-differential Lie triple systems and applications." AIMS Mathematics 8, no. 10 (2023): 25079–96. http://dx.doi.org/10.3934/math.20231280.

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<abstract>In this paper, we introduce the concept and representation of modified $ \lambda $-differential Lie triple systems. Next, we define the cohomology of modified $ \lambda $-differential Lie triple systems with coefficients in a suitable representation. As applications of the proposed cohomology theory, we study 1-parameter formal deformations and abelian extensions of modified $ \lambda $-differential Lie triple systems.</abstract>

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