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.

DOI: 10.14232/actasm-020-616-0

AMS Subject Classification (1991): 16E40, 16S80, 16W99

Keyword(s): involutive algebras, Hochschild cohomology, Rota--Baxter operators, deformations, dendriform algebras

received 16.6.2020, accepted 21.5.2021. (Registered under 616/2020.)