Rota–Baxter operators on involutive associative algebras
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Publication:5013136
DOI10.14232/ACTASM-020-616-0zbMATH Open1499.16027arXiv2006.09453OpenAlexW3205948799MaRDI QIDQ5013136
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Publication date: 27 November 2021
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/2006.09453
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