Leibniz Algebras and Lie Algebras

Abstract

This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.

Cited by in corpus (10)

• Unified products for Leibniz algebras. Applications
• A characterisation of Lie algebras amongst anti-commutative algebras
• The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras
• Bipartite graphs and the structure of finite-dimensional semisimple Leibniz algebras
• Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second type ${\mathcal{L}}^4$
• On a class of Leibniz Algebras
• (Bi)Hom-Leibniz algebras
• Gröbner-Shirshov bases theory and extensions of Leibniz superalgebras
• A class of Lie racks associated to symmetric Leibniz algebras
• Algebras of quotients and Martindale-like quotients of Leibniz algebras