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Journal articles on the topic 'Système de triple de Lie'

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Published: 26 April 2025

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1

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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2

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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3

Asif, Sania, and Zhixiang Wu. "Generalized Lie Triple Derivations of Lie Color Algebras and Their Subalgebras." Symmetry 13, no. 7 (July 16, 2021): 1280. http://dx.doi.org/10.3390/sym13071280.

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Consider a Lie color algebra, denoted by L. Our aim in this paper is to study the Lie triple derivations TDer(L) and generalized Lie triple derivations GTDer(L) of Lie color algebras. We discuss the centroids, quasi centroids and central triple derivations of Lie color algebras, where we show the relationship of triple centroids, triple quasi centroids and central triple derivation with Lie triple derivations and generalized Lie triple derivations of Lie color algebras L. A classification of Lie triple derivations algebra of all perfect Lie color algebras is given, where we prove that for a perfect and centerless Lie color algebra, TDer(L)=Der(L) and TDer(Der(L))=Inn(Der(L)).

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4

Asif, Sania, Lipeng Luo, Yanyong Hong, and Zhixiang Wu. "Conformal Triple Derivations and Triple Homomorphisms of Lie Conformal Algebras." Algebra Colloquium 30, no. 02 (June 2023): 263–80. http://dx.doi.org/10.1142/s1005386723000214.

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Let [Formula: see text] be a finite Lie conformal algebra. We investigate the conformal derivation algebra [Formula: see text], conformal triple derivation algebra [Formula: see text] and generalized conformal triple derivation algebra [Formula: see text], focusing mainly on the connections among these derivation algebras. We also give a complete classification of (generalized) conformal triple derivation algebras on all finite simple Lie conformal algebras. In particular, [Formula: see text], where [Formula: see text] is a finite simple Lie conformal algebra. But for [Formula: see text], we obtain a conclusion that is closely related to [Formula: see text]. Finally, we introduce the definition of a triple homomorphism of Lie conformal algebras. Triple homomorphisms of all finite simple Lie conformal algebras are also characterized.

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5

Biyogmam, Guy Roger. "LIE CENTRAL TRIPLE RACKS." International Electronic Journal of Algebra 17, no. 17 (June 1, 2015): 58. http://dx.doi.org/10.24330/ieja.266212.

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6

Li, Hailing, and Ying Wang. "Generalized Lie triple derivations." Linear and Multilinear Algebra 59, no. 3 (March 2011): 237–47. http://dx.doi.org/10.1080/03081080903350153.

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7

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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8

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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9

Brešar, M., M. Cabrera, M. Fošner, and A. R. Villena. "Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan–Banach algebras." Studia Mathematica 169, no. 3 (2005): 207–28. http://dx.doi.org/10.4064/sm169-3-1.

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10

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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11

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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12

Liu, Xiaohong, and Liangyun Chen. "The Centroid of a Lie Triple Algebra." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/404219.

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General results on the centroids of Lie triple algebras are developed. Centroids of the tensor product of a Lie triple algebra and a unitary commutative associative algebra are studied. Furthermore, the centroid of the tensor product of a simple Lie triple algebra and a polynomial ring is completely determined.

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13

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><p>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.</p></abstract>

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14

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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15

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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16

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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17

Lawson, Jimmie, and Yongdo Lim. "Lie semigroups with triple decompositions." Pacific Journal of Mathematics 194, no. 2 (June 1, 2000): 393–412. http://dx.doi.org/10.2140/pjm.2000.194.393.

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18

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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19

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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20

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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21

Jafari, Hossein, and Ali Madadi. "On the equality of triple derivations and derivations of lie algebras." Filomat 34, no. 7 (2020): 2439–49. http://dx.doi.org/10.2298/fil2007439j.

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Let L be a Lie algebra over a commutative ring with identity. In the present paper under some mild conditions on L, it is proved that every triple derivation of L is a derivation. In particular, we show that in perfect Lie algebras and free Lie algebras every triple derivation is a derivation. Finally we apply our results to show that every triple derivation of the Lie algebra of block upper triangular matrices is a derivation.

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22

Zhou, Jia, Liangyun Chen, and Yao Ma. "Triple derivations and triple homomorphisms of perfect Lie superalgebras." Indagationes Mathematicae 28, no. 2 (April 2017): 436–45. http://dx.doi.org/10.1016/j.indag.2016.11.012.

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23

Issa, A. Nourou. "Classifying two-dimensional hyporeductive triple algebra." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–10. http://dx.doi.org/10.1155/ijmms/2006/13527.

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Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e., generalized Lie triple systems) and two-dimensional real Bol algebras is given .

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24

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><p>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.</p></abstract>

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25

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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26

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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27

IZADI, JAVAD. "STABILITY OF LIE BRACKET OF TRIPLE JORDAN DERIVATIONS ON TRIPLE BANACH ALGEBRA." Journal of Inequalities and Special Functions 15, no. 4 (December 30, 2024): 15–25. https://doi.org/10.54379/jiasf-2024-4-2.

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This paper presents the mixed additive-Jensen equations and shows that a solution of it is a complex linear mapping. We also define the Lie bracket of triple Jordan derivations related to this equation in triple Banach algebra and investigate their properties. Lastly, we show the Hyers-Ulam (HU) stability of the mixed additive-Jensen equations and the Lie bracket of triple Jordan derivations on triple Banach algebra through the fixed point method, with control functions introduced by G˘avrut¸a and Rassias.

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28

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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29

Calderón Martín, Antonio Jesús, Cristina Draper Fontanals, and Cándido Martín González. "Gradings on Lie triple systems related to exceptional Lie algebras." Journal of Pure and Applied Algebra 217, no. 4 (April 2013): 672–88. http://dx.doi.org/10.1016/j.jpaa.2012.08.007.

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30

Kamiya, N. "The Nil Radical for Lie or Anti-Lie Triple Systems." Journal of Algebra 158, no. 1 (June 1993): 226–32. http://dx.doi.org/10.1006/jabr.1993.1131.

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31

Raza, Mohd Arif, Aisha Jabeen, and Tahani Al-Sobhi. "Lie triple derivation and Lie bi-derivation on quaternion rings." Miskolc Mathematical Notes 25, no. 1 (2024): 433. http://dx.doi.org/10.18514/mmn.2024.4413.

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In this study, we prove the existence of the central Lie bi-derivation for the ring with identity on the quaternion ring. We also describe the triple Lie derivation using the Jordan derivation on the aforementioned ring. An example is provided to demonstrate that our result is theoretically viable.

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32

Attan, Sylvain, and Donatien Gaparayi. "Hom-Hyporeductive Triple Algebras." Journal of Mathematical Sciences: Advances and Applications 65, no. 1 (April 10, 2021): 25–58. http://dx.doi.org/10.18642/jmsaa_7100122199.

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Hom-hyporeductive triple algebras are defined as a twisted generalization of hyporeductive triple algebras. Hom-hyporeductive triple algebras generalize right Hom-Lie-Yamaguti and right Hom-Bol algebras as the same way as hyporeductive triple algebras generalize right Lie-Yamaguti and right Bol algebras. It is shown that the category of Hom-hyporeductive triple algebras is closed under the process of taking nth derived binary-ternary Hom-algebras and by self-morphisms of binary-ternary algebras. Some examples of Hom-hyporeductive triple algebras are given.

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33

Benkovič, Dominik. "Lie Triple Derivations on Triangular Matrices." Algebra Colloquium 18, spec01 (December 2011): 819–26. http://dx.doi.org/10.1142/s1005386711000708.

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Let [Formula: see text] be the algebra of all n × n upper triangular matrices over a commutative unital ring [Formula: see text], and let [Formula: see text] be a 2-torsion free unital [Formula: see text]-bimodule. We show that every Lie triple derivation [Formula: see text] is a sum of a standard Lie derivation and an antiderivation.

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34

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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35

Zhou, Jianhua. "Triple Derivations of Perfect Lie Algebras." Communications in Algebra 41, no. 5 (May 20, 2013): 1647–54. http://dx.doi.org/10.1080/00927872.2011.649224.

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36

Li, Changjing, Xiaochun Fang, Fangyan Lu, and Ting Wang. "Lie Triple Derivable Mappings on Rings." Communications in Algebra 42, no. 6 (February 2014): 2510–27. http://dx.doi.org/10.1080/00927872.2012.763041.

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37

Zhou, Jianhua. "Triple Homomorphisms of Perfect Lie Algebras." Communications in Algebra 42, no. 9 (April 23, 2014): 3724–30. http://dx.doi.org/10.1080/00927872.2013.791987.

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38

Wang, Danni, and Zhankui Xiao. "Lie triple derivations of incidence algebras." Communications in Algebra 47, no. 5 (February 20, 2019): 1841–52. http://dx.doi.org/10.1080/00927872.2018.1523422.

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39

Xiao, Zhankui, and Feng Wei. "Lie triple derivations of triangular algebras." Linear Algebra and its Applications 437, no. 5 (September 2012): 1234–49. http://dx.doi.org/10.1016/j.laa.2012.04.015.

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40

Ji, Peisheng, and Lin Wang. "Lie triple derivations of TUHF algebras." Linear Algebra and its Applications 403 (July 2005): 399–408. http://dx.doi.org/10.1016/j.laa.2005.02.004.

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41

Zhang, Jian-Hua, Bao-Wei Wu, and Huai-Xin Cao. "Lie triple derivations of nest algebras." Linear Algebra and its Applications 416, no. 2-3 (July 2006): 559–67. http://dx.doi.org/10.1016/j.laa.2005.12.003.

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42

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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43

Bayara, Joseph, Amidou Konkobo, and Moussa Ouattara. "Algèbres De Lie Triple Sans Idempotent." Afrika Matematika 25, no. 4 (June 26, 2013): 1063–75. http://dx.doi.org/10.1007/s13370-013-0172-4.

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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

Ebrahimi, Sepideh. "Lie triple derivations on primitive rings." Asian-European Journal of Mathematics 08, no. 02 (June 2015): 1550019. http://dx.doi.org/10.1142/s1793557115500199.

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In this paper, we show that for each Lie triple derivation L on primitive ring R of characteristic not 2 with nontrivial idempotent, there exists an ordinary derivation D of R into a primitive ring [Formula: see text] containing R and additive mapping λ of R into the center of [Formula: see text] that annihilates commutators such that L(X) = D(X) + λ(X).

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47

Grabowski, Jan. "A triple construction for Lie bialgebras." Pacific Journal of Mathematics 221, no. 2 (October 1, 2005): 281–301. http://dx.doi.org/10.2140/pjm.2005.221.281.

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48

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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49

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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50

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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