Cohomology and deformations of O-operators on Hom-associative algebras

In this paper, we introduce the cohomology theory of O operators on Hom-associative algebras. This cohomology can also be viewed as the Hochschild cohomology of a certain Hom-associative algebra with coefficients in a suitable bimodule. Next, we study infinitesimal and formal deformations of an O-operator and show that they are governed by the above-defined cohomology. Furthermore, the notion of Nijenhuis elements associated with an O-operator is introduced to characterize trivial infinitesimal deformations. Moreover, we provide relevant constructions that twists objects on associative algebras to objects on Hom-associative algebras along morphisms. (c) 2022 Elsevier Inc. All rights reserved.