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Journal of Lie Theory 31 (2021), No. 2, 301--312
Copyright Heldermann Verlag 2021

On the Schur Multiplier and Covers of a Pair of Leibniz Algebras

Guy R. Biyogmam
Dept. of Mathematics, Georgia College & State University, Milledgeville, U.S.A.

Hesam Safa
Dept. of Mathematics, Faculty of Basic Sciences, University of Bojnord, Iran

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.

Keywords: Pair of Leibniz algebras, Schur multiplier, cover.

MSC: 17A32, 17B99.

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