Rota-Baxter operators on involutive associative algebras

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...

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Bibliographic Details
Main Author: Das Apurba
Format: Article
Published: 2021
Series:Acta scientiarum mathematicarum 87 No. 3-4
Kulcsszavak:Matematika, Rota-Baxter operátorok, Algebra
Subjects:
doi:10.14232/actasm-020-616-0

Online Access:http://acta.bibl.u-szeged.hu/75845
Description
Summary: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.
Physical Description:349-366
ISSN:2064-8316