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arXiv · 2010.01156

Cohomology and deformations of twisted Rota-Baxter operators and NS-algebras

Apurba Das
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Abstract

The aim of this paper is twofold. In the first part, we consider twisted Rota-Baxter operators on associative algebras that were introduced by Uchino as a noncommutative analogue of twisted Poisson structures. We construct an $L_\infty$-algebra whose Maurer-Cartan elements are given by twisted Rota-Baxter operators. This leads to cohomology associated to a twisted Rota-Baxter operator. This cohomology can be seen as the Hochschild cohomology of a certain associative algebra with coefficients in a suitable bimodule. We study deformations of twisted Rota-Baxter operators by means of the above-defined cohomology. Application is given to Reynolds operators. In the second part, we consider NS-algebras of Leroux that are related to twisted Rota-Baxter operators in the same way dendriform algebras are related to Rota-Baxter operators. We define cohomology of NS-algebras using multiplicative operads and study their deformations in terms of the cohomology.

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BibTeXRIS

Apurba Das. 2020-10-02. Cohomology and deformations of twisted Rota-Baxter operators and NS-algebras. https://arxiv.org/abs/2010.01156

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