On the schur multiplier and covers of a pair of leibniz algebras

Document Type

Article

Publication Date

1-1-2021

Publication Title

Journal of Lie Theory

Abstract

We utilize the notion of relative central extension on pairs of Leibniz algebras to study their Schur multipliers and covers. We provide some necessary conditions for detecting a certain class of covers of a pair of Leibniz algebras. In addition, we prove that every perfect pair of Leibniz algebras admits at least one cover. Moreover, we show that under certain conditions this cover is unique up to isomorphism. Finally, we prove that any two covers of a finite dimensional Leibniz algebra induce isoclinic pairs of Leibniz algebras.

Department

Mathematics

Volume Number

31

Issue Number

2

First Page

301

Last Page

312

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