The c-nilpotent Schur Lie-multiplier of Leibniz algebras

摘要

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 Lei bniz algebras. We prove the existence of c-Lie-s tem 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. (C) 2019 Elsevier B.V. All rights reserved.