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arXiv · 2006.09453

Rota-Baxter operators on involutive associative algebras

Apurba Das
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Abstract

In this paper, we consider Rota-Baxter operators on involutive associative algebras. We define cohomology for Rota-Baxter operators on involutive algebras that governs the formal deformation of the operator. This cohomology can be seen as the Hochschild cohomology of a certain involutive associative algebra with coefficients in a suitable involutive bimodule. We also relate this cohomology with the cohomology of involutive dendriform algebras. Finally, we show that the standard Fard-Guo construction of the functor from the category of dendriform algebras to the category of Rota-Baxter algebras restricts to the involutive case.

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Apurba Das. 2020-06-16. Rota-Baxter operators on involutive associative algebras. https://arxiv.org/abs/2006.09453

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