Some remarks on semisimple Leibniz algebras

DOI10.1016/j.jalgebra.2013.04.027zbMath1361.17007arXiv1201.5559OpenAlexW2022975552WikidataQ123250827 ScholiaQ123250827MaRDI QIDQ403133

A. Kh. Khudoyberdiyev, S. Gómez-Vidal, Bakhrom A. Omirov

Publication date: 29 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.5559

zbMATH Keywords

Lie algebrasLeibniz algebrassimplicitysolvable radicalsemisimplicityLevi's theorem

Mathematics Subject Classification ID

Structure theory for nonassociative algebras (17A60) Simple, semisimple, reductive (super)algebras (17B20) Leibniz algebras (17A32)

Related Items (20)

A new approach to Leibniz bialgebras ⋮ O-operators and related structures on Leibniz algebras ⋮ On the automorphism groups of some Leibniz algebras ⋮ Complete Leibniz algebras ⋮ Unnamed Item ⋮ Leibniz algebras associated with representations of filiform Lie algebras ⋮ On the endomorphisms and derivations of some Leibniz algebras ⋮ Some cohomologically rigid solvable Leibniz algebras ⋮ Some structure theories of Leibniz triple systems ⋮ Symplectic structures, product structures and complex structures on Leibniz algebras ⋮ The second cohomology group of simple Leibniz algebras ⋮ ON REPRESENTATIONS OF SYMMETRIC LEIBNIZ ALGEBRAS ⋮ Algorithmic method to obtain combinatorial structures associated with Leibniz algebras ⋮ Leibniz algebras whose semisimple part is related to \(sl_2\) ⋮ Leibniz Algebras with Invariant Bilinear Forms and Related Lie Algebras ⋮ Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second typeℒ² ⋮ Solvable extensions of naturally graded quasi-filiform Leibniz algebras of second type ℒ¹ and ℒ³ ⋮ Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems ⋮ Leibniz algebras as non-associative algebras ⋮ Right and left solvable extensions of an associative Leibniz algebra

Cites Work

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• On description of Leibniz algebras corresponding to \(sl _{2}\)
• Universal enveloping algebras of Leibniz algebras and (co)homology
• A noncommutative version of Lie algebras: Leibniz algebras
• On Leibniz homology
• Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras
• ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS
• Varieties of Nilpotent Complex Leibniz Algebras of Dimension Less than Five

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