Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256014 | Journal of Geometry and Physics | 2016 | 14 Pages |
Abstract
In the literature, most of the descriptions of different classes of Leibniz superalgebras (L=L0¯âL1¯,[â
,â
]) have been made by giving the multiplication table on the elements of a graded basis B={vk}kâK of L, in such a way that for any i,jâK we have [vi,vj]=λi,j[vj,vi]âFvk for some kâK, where F denotes the base field and λi,jâF. 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=L0¯âL1¯ admits a multiplicative basis then it is the direct sum L=â¨Î±Iα with any Iα=Iα,0¯âIα,1¯ being 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Helena Albuquerque, Elisabete Barreiro, Antonio J. Calderón MartÃn, José M. Sánchez Delgado,