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arXiv · 2207.13995

Relative Rota-Baxter Leibniz algebras, their characterization and cohomology

Apurba Das
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Abstract

Recently, relative Rota-Baxter (Lie/associative) algebras are extensively studied in the literature from cohomological points of view. In this paper, we consider relative Rota-Baxter Leibniz algebras (rRB Leibniz algebras) as the object of our study. We construct an $L_\infty$-algebra that characterizes rRB Leibniz algebras as its Maurer-Cartan elements. Then we define representations of an rRB Leibniz algebra and introduce cohomology with coefficients in a representation. As applications of cohomology, we study deformations and abelian extensions of rRB Leibniz algebras.

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Apurba Das. 2022-07-28. Relative Rota-Baxter Leibniz algebras, their characterization and cohomology. https://arxiv.org/abs/2207.13995

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