×

zbMATH — the first resource for mathematics

Semisimple Leibniz algebras, their derivations and automorphisms. (English) Zbl 07273647
Summary: The present paper is devoted to the description of the structures of finite-dimensional semisimple Leibniz algebras over complex numbers, their derivations and automorphisms.
MSC:
17A32 Leibniz algebras
17A60 Structure theory for nonassociative algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Loday, J-L., Une version non commutative des algèbres de Lie: les algèbres de Leibniz, Enseign Math, 39, 2, 269-293 (1993) · Zbl 0806.55009
[2] Albeverio, S.; Ayupov, ShA; Omirov, BA., On nilpotent and simple Leibniz algebras, Commun Algebra, 33, 159-172 (2005) · Zbl 1065.17001
[3] Albeverio, S.; Ayupov, ShA; Omirov, BA., Cartan subalgebras, weight spaces and criterion of solvability of finite dimensional Leibniz algebras, Rev Mat Complut, 19, 1, 183-195 (2006) · Zbl 1128.17001
[4] Balavoine, D., Déformations et rigidité géométrique des algèbres de Leibniz, Commun Algebra, 24, 3, 1017-1034 (1996) · Zbl 0855.17021
[5] Camacho, L.; Gómez, JR; González, AR; Omirov, BA., Naturally graded quasi-filiform Leibniz algebras, J Symbol Comput, 44, 527-539 (2009) · Zbl 1163.17003
[6] Camacho, L.; Gómez, JR; González, AJ, The classification of naturally graded p-filiform Leibniz algebras, Commun Algebra, 39, 1, 153-168 (2011) · Zbl 1215.17005
[7] Loday, J-L; Pirashvili, T., Leibniz representations of Leibniz algebras, J Algebra, 181, 414-425 (1996) · Zbl 0855.17018
[8] Omirov, BA., Conjugacy of Cartan subalgebras of complex finite dimensional Leibniz algebras, J Algebra, 302, 887-896 (2006) · Zbl 1128.17002
[9] Barnes, DW., On Levi’s theorem for Leibniz algebras, Bull Aust Math Soc, 86, 2, 184-185 (2012) · Zbl 1280.17002
[10] Casas, JM; Ladra, M.; Omirov, BA, Classification of solvable Leibniz algebras with null-filiform nilradical, Linear Multilinear Algebra, 61, 6, 758-774 (2013) · Zbl 1317.17003
[11] Jacobson, N., Lie algebras (1962), New York (NY): Interscience Publishers, Wiley, New York (NY) · Zbl 0121.27504
[12] Camacho, LM; Gómez-Vidal, S.; Omirov, BA, Leibniz algebras whose semisimple part is related to \(####\), Bull Malays Math Sci Soc, 40, 2, 599-615 (2017) · Zbl 1360.17003
[13] Ayupov, ShA, Kudaybergenov, KK, Omirov, AB.Local and 2-local derivations and automorphisms on simple Leibniz algebras. arXiv:1703.10506, 2017
[14] Zhelobenko, DP., Compact Lie groups and their representations (1973), New York (NY): AMS Providence, New York (NY)
[15] Humphreys, J., Introduction to Lie algebras and representation theory (1972), New York (NY): Springer, New York (NY) · Zbl 0254.17004
[16] Wan, Z., Lie algebras (1975), Braunschweig: Pergamon Press Ltd
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.