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ON REPRESENTATIONS OF SYMMETRIC LEIBNIZ ALGEBRAS

Part of: Other nonassociative rings and algebras Lie algebras and Lie superalgebras General nonassociative rings

Published online by Cambridge University Press:  23 May 2019

SAÏD BENAYADI
SAÏD BENAYADI*
Affiliation:
Université de Lorraine, Laboratoire IECL, CNRS UMR 7502, UFR MIM, 3 rue Augustin Frenel, BP 45112, 57073 Metz Cedex 03, France e-mail: [email protected]
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Abstract

We give a new and useful approach to study the representations of symmetric Leibniz algebras. Using this approach, we obtain some results on the representations of these algebras.

MSC classification

Primary: 17A32: Leibniz algebras 17B10: Representations, algebraic theory (weights)
Secondary: 17B05: Structure theory 17B30: Solvable, nilpotent (super)algebras 17D25: Lie-admissible algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Special Issue S1: Workshop on Nonassociative algebras and their applications , December 2020 , pp. S99 - S107
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

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References

Barnes, D., Some theorems on Leibniz algebras, Comm. Algebra 39 (2011), 2463–2472.CrossRefGoogle Scholar
Barreiro, E. and Benayadi, S., A new approach to Leibniz bialgebras, Algebr. Represent. Th. 19 (2016), 71–101.CrossRefGoogle Scholar
Benayadi, S. and Boucetta, M., Special bi-invariant linear connections on Lie groups and finite dimensional Poisson structures, Differ. Geom. Appl. 36 (2014), 66–89.CrossRefGoogle Scholar
Benayadi, S. and Hidri, S., Quadratic Leibniz algebras, J. Lie Theory 24(3), 737–759.Google Scholar
Bloh, A., On a generalization of the concept of a Lie algebra, Dokl. Akad. Nauk. USSR 165 (1965), 471–473.Google Scholar
Bloh, A., Cartan-Eilenberg homology theory for a generalized class of Lie algebras, Dokl. Akad. Nauk SSSR 175 (1967), 824–826.Google Scholar
Bloh, A., A certain generalization of the concept of Lie algebra, Uch. Zap. Moskov. Gos. Ped. Inst. 375 (1971), 9–20 (in Russian).Google Scholar
Casas, J. M., Ladra, M., Omirov, B. A. and Karimjanov, I. A., Classification of solvable Leibniz algebras with naturally graded filiform nilradical, Linear Algebra Appl . 438(7) (2013), 2973–3000.CrossRefGoogle Scholar
Covez, S., The local integration of Leibniz algebras, Ann. Inst. Fourier (Grenoble) 63(1) (2013), 1–35.CrossRefGoogle Scholar
Cuvier, C., Algèbres de Leibnitz: Définition, propriétées, Ann. Sci. École Norm. Sup. 27(4) (1994), 1–45.CrossRefGoogle Scholar
Fialowski, A., Magnin, L. and Mandan, A., About Leibniz cohomology and deformations of Lie algebras, J. Algebra 383 (2013), 63–77.CrossRefGoogle Scholar
Gòmez-Vidal, S., Khudoyberdiyev, A. Kh. and Omirov, B. A., Some remarks on semisimple Leibniz algebras, J. Algebra 410 (2014), 526–540.Google Scholar
Hedges, A. and Stitzinger, E., More on the Frattini subalgebra of a Leibniz algebra, arXiv:1206.5707v2 [math.RA] (2013).Google Scholar
Loday, J.-L., Une version non commutative des algèbres de Lie: les algèbres de Leibniz. (French) [A noncommutative version of Lie algebras: the Leibniz algebras], Enseign. Math, 39(3-4) (1993), 269–293.Google Scholar
Loday, J.-L. and Pirashvili, T., Universal enveloping algebras of Leibniz algebras and (co)homology, Math. Ann. 296 (1993), 139–158.CrossRefGoogle Scholar
Mason, G. and Yamskulna, G., Leibniz algebras and Lie algebras, Symmetry Integrability Geom. Methods Appl. (SIGMA) 9 (2013), Paper 063, 10 p.Google Scholar
Schafer, R. D., An introduction to nonassociative algebras (Academic Press, New York, 1966).Google Scholar
Tauvel, P. and Yu, R. W. T., Lie algebras and algebraic groups (Springer-Verlag, Berlin Heidelberg, 2005).CrossRefGoogle Scholar