Article
The c-nilpotent Schur Lie-multiplier of Leibniz algebras
Journal of Geometry and Physics
(2019)
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.
Disciplines
Publication Date
2019
DOI
https://doi.org/10.1016/j.geomphys.2018.12.021
Citation Information
Guy Biyogmam and Juane M Casas. "The c-nilpotent Schur Lie-multiplier of Leibniz algebras" Journal of Geometry and Physics Vol. 138 (2019) p. 55 - 69 Available at: http://works.bepress.com/guy-biyogmam/21/