Bimodules over relative Rota-Baxter algebras and cohomologies

Apurba Das; Satyendra Kumar Mishra

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arXiv · 2207.10954

Bimodules over relative Rota-Baxter algebras and cohomologies

Apurba Das·Satyendra Kumar Mishra

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Abstract

A relative Rota-Baxter algebra is a generalization of a Rota-Baxter algebra. Relative Rota-Baxter algebras are closely related to dendriform algebras. In this paper, we introduce bimodules over a relative Rota-Baxter algebra that fits with the representations of dendriform algebras. We define the cohomology of a relative Rota-Baxter algebra with coefficients in a bimodule and then study abelian extensions of relative Rota-Baxter algebras in terms of the second cohomology group. Finally, we consider homotopy relative Rota-Baxter algebras and classify skeletal homotopy relative Rota-Baxter algebras in terms of the above-defined cohomology.

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BibTeX RIS

Apurba Das, Satyendra Kumar Mishra. 2022-07-22. Bimodules over relative Rota-Baxter algebras and cohomologies. https://arxiv.org/abs/2207.10954

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