Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	The structure of Leibniz superalgebras admitting a multiplicative basis
Publication Date:	2016-07-19
Authors:	- Helena Albuquerque - Maria Elisabete Barreiro - Antonio Jesus Calderón - José M. Sánchez-Delgado
Abstract:	In the literature, most of the descriptions of different classes of Leibniz superalgebras (L = L0 L1; [; ]) have been made by given the multiplication table on the elements of a graded basis B = fvkgk2K of L, in such a way that for any i; j 2 K we have [vi; vj ] = i;j [vj ; vi] 2 Fvk for some k 2 K, where F denotes the base field and i;j 2 F. In order to give a unifying viewpoint of all these classes of algebras we introduce the category of Leibniz superalgebras admitting a multiplicative basis and study its structure. We show that if a Leibniz superalgebra L = L0L1 admits a multiplicative basis then it is the direct sum L = L I with any I = I;0I;1 a well described ideal of L admitting a multiplicative basis inherited from B. Also the B-simplicity of L is characterized in terms of J-connections.
Institution:	DMUC 16-36
Online version:	http://www.mat.uc.pt...prints/eng_2016.html
Download:	Not available