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Journal articles on the topic 'Complex semisimple Lie algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

ARDAKOV, KONSTANTIN, and IAN GROJNOWSKI. "KRULL DIMENSION OF AFFINOID ENVELOPING ALGEBRAS OF SEMISIMPLE LIE ALGEBRAS." Glasgow Mathematical Journal 55, A (2013): 7–26. http://dx.doi.org/10.1017/s0017089513000487.

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AbstractUsing Beilinson–Bernstein localisation, we give another proof of Levasseur's theorem on the Krull dimension of the enveloping algebra of a complex semisimple Lie algebra. The proof also extends to the case of affinoid enveloping algebras.

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2

ONDRUS, MATTHEW, and EMILIE WIESNER. "WHITTAKER MODULES FOR THE VIRASORO ALGEBRA." Journal of Algebra and Its Applications 08, no. 03 (2009): 363–77. http://dx.doi.org/10.1142/s0219498809003370.

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Whittaker modules have been well studied in the setting of complex semisimple Lie algebras. Their definition can easily be generalized to certain other Lie algebras with triangular decomposition, including the Virasoro algebra. We define Whittaker modules for the Virasoro algebra and obtain analogues to several results from the classical setting, including a classification of simple Whittaker modules by central characters and composition series for general Whittaker modules.

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3

ZHANG, SHOUCHUAN, YAO-ZHONG ZHANG, and HUI-XIANG CHEN. "CLASSIFICATION OF PM QUIVER HOPF ALGEBRAS." Journal of Algebra and Its Applications 06, no. 06 (2007): 919–50. http://dx.doi.org/10.1142/s0219498807002569.

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We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter–Drinfeld modules and their corresponding Nichols algebras. In particular, when the ground-field k is the complex field and G is a finite abelian group, we classify quiver Hopf algebras over G, multiple Taft algebras over G and Nichols algebras in [Formula: see text]. We show that the quantum enveloping algebra of a complex semisimple Lie algebra is a quotient of a semi-path Hopf algebra.

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4

Cheung, Wai-Shun, and Tin-Yau Tam. "Star-Shapedness and K-Orbits in Complex Semisimple Lie Algebras." Canadian Mathematical Bulletin 54, no. 1 (2011): 44–55. http://dx.doi.org/10.4153/cmb-2010-097-7.

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AbstractGiven a complex semisimple Lie algebra is a compact real form of g), let be the orthogonal projection (with respect to the Killing form) onto the Cartan subalgebra , where t is a maximal abelian subalgebra of . Given x ∈ g, we consider π(Ad(K)x), where K is the analytic subgroup G corresponding to , and show that it is star-shaped. The result extends a result of Tsing. We also consider the generalized numerical range f (Ad(K)x), where f is a linear functional on g. We establish the star-shapedness of f (Ad(K)x) for simple Lie algebras of type B.

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5

Reeder, Mark. "Exterior Powers of the Adjoint Representation." Canadian Journal of Mathematics 49, no. 1 (1997): 133–59. http://dx.doi.org/10.4153/cjm-1997-007-1.

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6

Helmke, Uwe, and Martin Kleinsteuber. "A differential equation for diagonalizing complex semisimple Lie algebra elements." Systems & Control Letters 59, no. 1 (2010): 72–78. http://dx.doi.org/10.1016/j.sysconle.2009.12.001.

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7

BISWAS, INDRANIL, and PRALAY CHATTERJEE. "ON THE EXACTNESS OF KOSTANT–KIRILLOV FORM AND THE SECOND COHOMOLOGY OF NILPOTENT ORBITS." International Journal of Mathematics 23, no. 08 (2012): 1250086. http://dx.doi.org/10.1142/s0129167x12500863.

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We give a criterion for the Kostant–Kirillov form on an adjoint orbit in a real semisimple Lie group to be exact. We explicitly compute the second cohomology of all the nilpotent adjoint orbits in every complex simple Lie algebra.

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8

Djoković, D. Ž. "On real forms of complex semisimple Lie algebras." Aequationes mathematicae 58, no. 1-2 (1999): 73–84. http://dx.doi.org/10.1007/s000100050008.

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9

Djoković, D. Ž. "On real forms of complex semisimple Lie algebras." Aequationes Mathematicae 58, no. 1-2 (1999): 73–84. http://dx.doi.org/10.1007/s000100050094.

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10

BARANOV, A. A., and A. E. ZALESSKII. "PLAIN REPRESENTATIONS OF LIE ALGEBRAS." Journal of the London Mathematical Society 63, no. 3 (2001): 571–91. http://dx.doi.org/10.1017/s0024610701002101.

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In this paper we study representations of finite dimensional Lie algebras. In this case representations are not necessarily completely reducible. As the general problem is known to be of enormous complexity, we restrict ourselves to representations that behave particularly well on Levi subalgebras. We call such representations plain (Definition 1.1). Informally, we show that the theory of plain representations of a given Lie algebra L is equivalent to representation theory of finitely many finite dimensional associative algebras, also non-semisimple. The sense of this is to distinguish represe

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11

Garibaldi, Skip, and Daniel K. Nakano. "Bilinear and Quadratic Forms on Rational Modules of Split Reductive Groups." Canadian Journal of Mathematics 68, no. 2 (2016): 395–421. http://dx.doi.org/10.4153/cjm-2015-042-5.

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AbstractThe representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the questions of whether a given complex representation is symplectic or orthogonal have been solved since at least the 1950s. Similar results for Weyl modules of split reductive groups over fields of characteristic different from z hold by using similar proofs. This paper considers analogues of these results for simple, induced, and tilting modules of split reductive groups over fields of prime characteristic as

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12

Nahlus, Nazih. "Homomorphisms of Lie Algebras of Algebraic Groups and Analytic Groups." Canadian Mathematical Bulletin 38, no. 3 (1995): 352–59. http://dx.doi.org/10.4153/cmb-1995-051-7.

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AbstractLet be a Lie algebra homomorphism from the Lie algebra of G to the Lie algebra of H in the following cases: (i) G and H are irreducible algebraic groups over an algebraically closed field of characteristic 0, or (ii) G and H are linear complex analytic groups. In this paper, we present some equivalent conditions for ϕ to be a differential in the above two cases. That is, ϕ is the differential of a morphism of algebraic groups or analytic groups as appropriate.In the algebraic case, for example, it is shown that ϕ is a differential if and only if ϕ preserves nilpotency, semisimplicity,

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13

Nasrin, Salma. "Corwin–Greenleaf multiplicity functions for complex semisimple symmetric spaces." International Journal of Mathematics 26, no. 05 (2015): 1550039. http://dx.doi.org/10.1142/s0129167x15500391.

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Let Gℂ be a complex simple Lie group, GU a compact real form, and [Formula: see text] the natural projection between the dual of the Lie algebras. We prove that, for any coadjoint orbit [Formula: see text] of GU, the intersection of [Formula: see text] with a coadjoint orbit [Formula: see text] of Gℂ is either an empty set or a single orbit of GU if [Formula: see text] is isomorphic to a complex symmetric space.

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14

Han, Gang, and Daowei Wen. "Restrictions of Symmetric Invariants of a Complex Semisimple Lie Algebra and Some Applications." Communications in Algebra 42, no. 9 (2014): 3782–94. http://dx.doi.org/10.1080/00927872.2013.795576.

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15

Tam, Tin-Yau, and Wai-Shun Cheung. "The K-orbit of a normal element in a complex semisimple Lie algebra." Pacific Journal of Mathematics 238, no. 2 (2008): 387–98. http://dx.doi.org/10.2140/pjm.2008.238.387.

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16

Wang, Wei, and Chunguang Xia. "Structure of a Class of Rank Two Lie Conformal Algebras." Algebra Colloquium 28, no. 01 (2021): 169–80. http://dx.doi.org/10.1142/s1005386721000158.

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Let [Formula: see text] be a complex number, and a class of non-semisimple and non-solvable rank two Lie conformal algebras [Formula: see text] are introduced. In this paper, conformal derivations, conformal quasiderivations, generalized conformal derivations and conformal biderivations of [Formula: see text] are studied. Besides, central extensions and conformal modules of rank one of [Formula: see text] are determined.

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17

Enriquez, B. "Quasi-Hopf algebras associated with semisimple Lie algebras and complex curves." Selecta Mathematica 9, no. 1 (2003): 1–61. http://dx.doi.org/10.1007/s00029-003-0317-7.

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18

Lopes, Samuel A. "Separation of Variables for." Canadian Mathematical Bulletin 48, no. 4 (2005): 587–600. http://dx.doi.org/10.4153/cmb-2005-054-8.

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AbstractLet be the positive part of the quantized enveloping algebra . Using results of Alev–Dumas and Caldero related to the center of , we show that this algebra is free over its center. This is reminiscent of Kostant's separation of variables for the enveloping algebra U(g) of a complex semisimple Lie algebra g, and also of an analogous result of Joseph–Letzter for the quantum algebra Ŭq(g). Of greater importance to its representation theory is the fact that is free over a larger polynomial subalgebra N in n variables. Induction from N to provides infinite-dimensional modules with good prop

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19

Wüstner, Michael. "On the Surjectivity of the Exponential Function of Complex Algebraic, Complex Semisimple, and Complex Splittable Lie Groups." Journal of Algebra 184, no. 3 (1996): 1082–92. http://dx.doi.org/10.1006/jabr.1996.0300.

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20

Penkov, Ivan, and Gregg Zuckerman. "Construction of Generalized Harish-Chandra Modules with Arbitrary Minimal -Type." Canadian Mathematical Bulletin 50, no. 4 (2007): 603–9. http://dx.doi.org/10.4153/cmb-2007-059-5.

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AbstractLet be a semisimple complex Lie algebra and ⊂ be any algebraic subalgebra reductive in . For any simple finite dimensional -module V, we construct simple (, )-modules M with finite dimensional -isotypic components such that V is a -submodule of M and the Vogan norm of any simple -submodule V′ ⊂ M,V′ ≄ V, is greater than the Vogan norm of V. The (, )-modules M are subquotients of the fundamental series of (, )-modules.

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21

Djoković, Dragomir Ž. "On conjugacy classes of elements of finite order in complex semisimple lie groups." Journal of Pure and Applied Algebra 35 (1985): 1–13. http://dx.doi.org/10.1016/0022-4049(85)90026-x.

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22

Shi, Zhiyong. "Existence and dimensionality of simple weight modules for quantum enveloping algebras." Bulletin of the Australian Mathematical Society 48, no. 1 (1993): 35–40. http://dx.doi.org/10.1017/s0004972700015434.

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We give sufficient and necessary conditions for simple modules of the quantum group or the quantum enveloping algebra Uq(g) to have weight space decompositions, where g is a semisimple Lie algebra and q is a nonzero complex number. We show that(i) if q is a root of unity, any simple module of Uq(g) is finite dimensional, and hence is a weight module;(ii) if q is generic, that is, not a root of unity, then there are simple modules of Uq(g) which do not have weight space decompositions.Also the group of units of Uq(g) is found.

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23

Johnson, B. E. "Weak amenability of group algebras of connected complex semisimple Lie groups." Proceedings of the American Mathematical Society 111, no. 1 (1991): 177. http://dx.doi.org/10.1090/s0002-9939-1991-1023344-6.

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24

Ðoković, Dragomir Ž., and Tin-Yau Tam. "Some Questions about Semisimple Lie Groups Originating in Matrix Theory." Canadian Mathematical Bulletin 46, no. 3 (2003): 332–43. http://dx.doi.org/10.4153/cmb-2003-035-1.

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AbstractWe generalize the well-known result that a square traceless complex matrix is unitarily similar to a matrix with zero diagonal to arbitrary connected semisimple complex Lie groups G and their Lie algebras under the action of a maximal compact subgroup K of G. We also introduce a natural partial order on : x ≤ y if f (K · x) ⊆ f (K · y) for all f 2 *, the complex dual of . This partial order is K-invariant and induces a partial order on the orbit space /K. We prove that, under some restrictions on , the set f (K · x) is star-shaped with respect to the origin.

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25

Douglass, J. Matthew, and Gerhard Röhrle. "Invariants of reflection groups, arrangements, and normality of decomposition classes in Lie algebras." Compositio Mathematica 148, no. 3 (2012): 921–30. http://dx.doi.org/10.1112/s0010437x11007512.

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AbstractSuppose that W is a finite, unitary, reflection group acting on the complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in W, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism from the algebra of W-invariant polynomial functions on V to the algebra of C-invariant functions on X. In this note we consider the special case when W is a Coxeter group, V is the complexified reflection representation of W, and X is in the lattice of the arrangement of W, and give a simple, combinatorial characterization of when the res

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26

Abe, Noriyuki. "On the existence of homomorphisms between principal series representations of complex semisimple Lie groups." Journal of Algebra 330, no. 1 (2011): 468–81. http://dx.doi.org/10.1016/j.jalgebra.2010.11.012.

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27

BRÜSTLE, TH, S. KÖNIG, and V. MAZORCHUK. "THE COINVARIANT ALGEBRA AND REPRESENTATION TYPES OF BLOCKS OF CATEGORY O." Bulletin of the London Mathematical Society 33, no. 6 (2001): 669–81. http://dx.doi.org/10.1112/s0024609301008529.

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Let [Gfr ] be a finite-dimensional semisimple Lie algebra over the complex numbers. Let A be the finite-dimensional algebra of a (regular or singular) block of the BGG-category [Oscr ] . By results of Soergel, A has a combinatorial description in terms of a subalgebra C0 of the coinvariant algebra C. König and Mazorchuk have constructed an embedding from C0-mod into the category [Fscr ](Δ) of A-modules having a Verma flag. This is the main tool for the classification of [Fscr ] (Δ) into finite, tame and wild representation types presented here. As a consequence a classification of A-mod into f

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28

Irving, Ronald S. "Shuffled Verma Modules and Principal Series Modules over Complex Semisimple Lie Algebras." Journal of the London Mathematical Society s2-48, no. 2 (1993): 263–77. http://dx.doi.org/10.1112/jlms/s2-48.2.263.

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29

Han, Gang. "Symmetric subalgebras noncohomologous to zero in a complex semisimple Lie algebra and restrictions of symmetric invariants." Journal of Algebra 319, no. 4 (2008): 1809–21. http://dx.doi.org/10.1016/j.jalgebra.2007.06.038.

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30

ARVANITOYEORGOS, ANDREAS. "GEOMETRY OF FLAG MANIFOLDS." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (2006): 957–74. http://dx.doi.org/10.1142/s0219887806001399.

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A flag manifold is a homogeneous space M = G/K, where G is a compact semisimple Lie group, and K the centralizer of a torus in G. Equivalently, M can be identified with the adjoint orbit Ad (G)w of an element w in the Lie algebra of G. We present several aspects of flag manifolds, such as their classification in terms of painted Dynkin diagrams, T-roots and G-invariant metrics, and Kähler metrics. We give a Lie-theoretic expression of the Ricci tensor in M, hence reducing the Einstein equation on flag manifolds into an algebraic system of equations, which can be solved in several cases. A flag

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31

LETZTER, EDWARD S. "NONCOMMUTATIVE IMAGES OF COMMUTATIVE SPECTRA." Journal of Algebra and Its Applications 07, no. 05 (2008): 535–52. http://dx.doi.org/10.1142/s0219498808002941.

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We initiate a unified, axiomatic study of noncommutative algebras R whose prime spectra are, in a natural way, finite unions of commutative noetherian spectra. Our results illustrate how these commutative spectra can be functorially "sewn together" to form Spec R. In particular, we construct a bimodule-determined functor Mod Z → Mod R, for a suitable commutative noetherian ring Z, from which there follows a finite-to-one, continuous surjection Spec Z → Spec R. Algebras satisfying the given axiomatic framework include PI algebras finitely generated over fields, noetherian PI algebras, envelopin

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32

Cavallin, Mikaël. "An algorithm for computing weight multiplicities in irreducible modules for complex semisimple Lie algebras." Journal of Algebra 471 (February 2017): 492–510. http://dx.doi.org/10.1016/j.jalgebra.2016.08.044.

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33

KOBAK, PIOTR Z., and ANDREW SWANN. "CLASSICAL NILPOTENT ORBITS AS HYPERKÄHLER QUOTIENTS." International Journal of Mathematics 07, no. 02 (1996): 193–210. http://dx.doi.org/10.1142/s0129167x96000116.

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We show that on an arbitrary nilpotent orbit [Formula: see text] in [Formula: see text] where [Formula: see text] is a direct sum of classical simple Lie algebras, there is a G-invariant hyperKähler structure obtainable as a hyperKäher quotient of the flat hyperKähler manifold ℝ4N≅ℍN. Coïncidences between various low-dimensional simple Lie groups lead to some nilpotent orbits being described as hyperKähler quotients (in some cases in fact finite quotients) of other nilpotent orbits. For example, from the construction we are able to read off pairs of orbits [Formula: see text] in different clas

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34

Pérez, Claudia, and Daniel Rivera. "Serre type relations for complex semisimple Lie algebras associated to positive definite quasi-Cartan matrices." Linear Algebra and its Applications 567 (April 2019): 14–44. http://dx.doi.org/10.1016/j.laa.2018.12.032.

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35

CROOKS, PETER. "AN EQUIVARIANT DESCRIPTION OF CERTAIN HOLOMORPHIC SYMPLECTIC VARIETIES." Bulletin of the Australian Mathematical Society 97, no. 2 (2018): 207–14. http://dx.doi.org/10.1017/s0004972717001095.

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Varieties of the form$G\times S_{\!\text{reg}}$, where$G$is a complex semisimple group and$S_{\!\text{reg}}$is a regular Slodowy slice in the Lie algebra of$G$, arise naturally in hyperkähler geometry, theoretical physics and the theory of abstract integrable systems. Crooks and Rayan [‘Abstract integrable systems on hyperkähler manifolds arising from Slodowy slices’,Math. Res. Let., to appear] use a Hamiltonian$G$-action to endow$G\times S_{\!\text{reg}}$with a canonical abstract integrable system. To understand examples of abstract integrable systems arising from Hamiltonian$G$-actions, we c

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36

Moody, R. V., and J. Patera. "Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight Lattices." Canadian Journal of Mathematics 47, no. 3 (1995): 573–605. http://dx.doi.org/10.4153/cjm-1995-031-2.

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AbstractWe give a uniform description, in terms of Coxeter diagrams, of the Voronoi domains of the root and weight lattices of any semisimple Lie algebra. This description provides a classification not only of all the facets of these Voronoi domains but simultaneously a classification of their dual or Delaunay cells and their facets. It is based on a much more general theory that we develop here providing the same sort of information in the setting of chamber geometries defined by arbitrary reflection groups. These generalized kaleidoscopes include the classical spherical, Euclidean, and hyper

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37

Abe, Takuro, Tatsuya Horiguchi, Mikiya Masuda, Satoshi Murai, and Takashi Sato. "Hessenberg varieties and hyperplane arrangements." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 764 (2020): 241–86. http://dx.doi.org/10.1515/crelle-2018-0039.

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AbstractGiven a semisimple complex linear algebraic group {{G}} and a lower ideal I in positive roots of G, three objects arise: the ideal arrangement {\mathcal{A}_{I}}, the regular nilpotent Hessenberg variety {\operatorname{Hess}(N,I)}, and the regular semisimple Hessenberg variety {\operatorname{Hess}(S,I)}. We show that a certain graded ring derived from the logarithmic derivation module of {\mathcal{A}_{I}} is isomorphic to {H^{*}(\operatorname{Hess}(N,I))} and {H^{*}(\operatorname{Hess}(S,I))^{W}}, the invariants in {H^{*}(\operatorname{Hess}(S,I))} under an action of the Weyl group W of

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38

PANYUSHEV, DMITRI I., and OKSANA S. YAKIMOVA. "NILPOTENT SUBSPACES AND NILPOTENT ORBITS." Journal of the Australian Mathematical Society 106, no. 1 (2018): 104–26. http://dx.doi.org/10.1017/s1446788718000071.

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Let $G$ be a semisimple complex algebraic group with Lie algebra $\mathfrak{g}$. For a nilpotent $G$-orbit ${\mathcal{O}}\subset \mathfrak{g}$, let $d_{{\mathcal{O}}}$ denote the maximal dimension of a subspace $V\subset \mathfrak{g}$ that is contained in the closure of ${\mathcal{O}}$. In this note, we prove that $d_{{\mathcal{O}}}\leq {\textstyle \frac{1}{2}}\dim {\mathcal{O}}$ and this upper bound is attained if and only if ${\mathcal{O}}$ is a Richardson orbit. Furthermore, if $V$ is $B$-stable and $\dim V={\textstyle \frac{1}{2}}\dim {\mathcal{O}}$, then $V$ is the nilradical of a polaris

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39

Marrani, Alessio, Fabio Riccioni, and Luca Romano. "Real weights, bound states and duality orbits." International Journal of Modern Physics A 31, no. 01 (2016): 1550218. http://dx.doi.org/10.1142/s0217751x15502188.

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We show that the duality orbits of extremal black holes in supergravity theories with symmetric scalar manifolds can be derived by studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the duality symmetry group. The weight vectors always correspond to weights that are real, where the reality properties are derived from the Tits–Satake diagram that identifies the real form of the Lie algebra of the duality symmetry group. Both [Formula: see text] magic Maxwell–Einstein supergravities and the

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40

Kiranagi, B. S., Ranjitha Kumar, and G. Prema. "On completely semisimple Lie algebra bundles." Journal of Algebra and Its Applications 14, no. 02 (2014): 1550009. http://dx.doi.org/10.1142/s0219498815500097.

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We study semisimple, completely semisimple Lie algebra bundles in terms of characteristic ideal bundles following Seligman. Further decomposition theorem for Lie algebra bundles over any field is proved following Dieudonné.

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41

de Graaf, Willem A. "Constructing semisimple subalgebras of semisimple Lie algebras." Journal of Algebra 325, no. 1 (2011): 416–30. http://dx.doi.org/10.1016/j.jalgebra.2010.10.021.

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42

Littelmann, Peter. "A Plactic Algebra for Semisimple Lie Algebras." Advances in Mathematics 124, no. 2 (1996): 312–31. http://dx.doi.org/10.1006/aima.1996.0085.

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43

Broer, Abraham. "Decomposition Varieties in Semisimple Lie Algebras." Canadian Journal of Mathematics 50, no. 5 (1998): 929–71. http://dx.doi.org/10.4153/cjm-1998-048-6.

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AbstractThe notion of decompositon class in a semisimple Lie algebra is a common generalization of nilpotent orbits and the set of regular semisimple elements.We prove that the closure of a decomposition class has many properties in common with nilpotent varieties, e.g., its normalization has rational singularities.The famous Grothendieck simultaneous resolution is related to the decomposition class of regular semisimple elements. We study the properties of the analogous commutative diagrams associated to an arbitrary decomposition class.

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44

Burde, Dietrich, and Vsevolod Gubarev. "Decompositions of algebras and post-associative algebra structures." International Journal of Algebra and Computation 30, no. 03 (2019): 451–66. http://dx.doi.org/10.1142/s0218196720500071.

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We introduce post-associative algebra structures and study their relationship to post-Lie algebra structures, Rota–Baxter operators and decompositions of associative algebras and Lie algebras. We show several results on the existence of such structures. In particular, we prove that there exists no post-Lie algebra structure on a pair [Formula: see text], where [Formula: see text] is a simple Lie algebra and [Formula: see text] is a reductive Lie algebra, which is not isomorphic to [Formula: see text]. We also show that there is no post-associative algebra structure on a pair [Formula: see text

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45

de Graaf, W. A. "Calculating the structure of a semisimple Lie algebra." Journal of Pure and Applied Algebra 117-118 (May 1997): 319–29. http://dx.doi.org/10.1016/s0022-4049(97)00016-9.

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46

Chloup, Véronique. "Bialgebra structures on a real semisimple Lie algebra." Bulletin of the Belgian Mathematical Society - Simon Stevin 2, no. 3 (1995): 265–78. http://dx.doi.org/10.36045/bbms/1103408720.

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47

Caenepeel, Frederik. "Glider representations of chains of semisimple Lie algebra." Communications in Algebra 46, no. 11 (2018): 4985–5005. http://dx.doi.org/10.1080/00927872.2018.1459652.

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48

Elduque, Alberto. "Lie Superalgebras with Semisimple Even Part." Journal of Algebra 183, no. 3 (1996): 649–63. http://dx.doi.org/10.1006/jabr.1996.0237.

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49

Burde, Dietrich, and Karel Dekimpe. "Post-Lie Algebra Structures and Generalized Derivations of Semisimple Lie Algebras." Moscow Mathematical Journal 13, no. 1 (2013): 1–18. http://dx.doi.org/10.17323/1609-4514-2013-13-1-1-18.

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50

Xu, Maosen, Yan Tan, and Zhixiang Wu. "Cohomology of Lie Conformal Algebra Vir⋉Cur g." Algebra Colloquium 28, no. 03 (2021): 507–20. http://dx.doi.org/10.1142/s1005386721000390.

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Abstract:

In this article, we compute cohomology groups of the semisimple Lie conformal algebra [Formula: see text] with coefficients in its irreducible modules for a finite-dimensional simple Lie algebra [Formula: see text].

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