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arXiv · 1710.10173

The c-Nilpotent Shur Lie-Multiplier of Leibniz Algebras

G. R. Biyogmam·J. M. Casas
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Abstract

We introduce the notion of c-nilpotent Schur Lie-multiplier of Leibniz algebras. We obtain exact sequences and formulas of the dimensions of the underlying vector spaces relating the c-nilpotent Schur Lie-multiplier of a Leibniz algebra Q and its quotient by a two-sided ideal. These tools are used to characterize Lie-nilpotency and c-Lie-stem covers of Leibniz algebras. We prove the existence of c-Lie-stem covers for finite dimensional Leibniz algebras and the non existence of c-covering on certain Lie-nilpotent Leibniz algebras with non trivial c-nilpotent Schur Lie-multiplier, and we provide characterizations of c-Lie-capability of Leibniz algebras by means of both their c-Lie-characteristic ideal and c-nilpotent Schur Lie-multiplier.

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BibTeXRIS

G. R. Biyogmam, J. M. Casas. 2017-10-26. The c-Nilpotent Shur Lie-Multiplier of Leibniz Algebras. https://arxiv.org/abs/1710.10173

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