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arXiv · 2306.06105

Cohomology and deformations of compatible Leibniz algebras

RB Yadav·Rinkila Bhutia·Namita Behera
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Abstract

In this paper we study a cohomology theory of compatible Leibniz algebra. We construct a graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible Leibniz algebras. Using this, we study cohomology, infinitisimal deformations, Nijenhuis operator and their relation for compatible leibniz algebras. Finally using cohomology of compatible Leibniz algebra with coefficients in an arbitrary representation we study the abelian extensions of compatible Leibniz algebra.

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RB Yadav, Rinkila Bhutia, Namita Behera. 2023-05-08. Cohomology and deformations of compatible Leibniz algebras. https://arxiv.org/abs/2306.06105

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