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arXiv · 2305.01025

On compatible Leibniz algebras

Abdenacer Makhlouf·Ripan Saha
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Abstract

In this paper, we study compatible Leibniz algebras. We characterize compatible Leibniz algebras in terms of Maurer-Cartan elements of a suitable differential graded Lie algebra. We define a cohomology theory of compatible Leibniz algebras which in particular controls a one-parameter formal deformation theory of this algebraic structure. Motivated by a classical application of cohomology, we moreover study the abelian extension of compatible Leibniz algebras.

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Abdenacer Makhlouf, Ripan Saha. 2023-05-01. On compatible Leibniz algebras. https://arxiv.org/abs/2305.01025

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