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

Abstract

In this paper, we introduce the cohomology theory of $\mathcal{O}$-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 $\mathcal{O}$-operator and show that they are governed by the above-defined cohomology. Furthermore, the notion of Nijenhuis elements associated with an $\mathcal{O}$-operator is introduced to characterize trivial infinitesimal deformations.

arXiv admin note: substantial text overlap with arXiv:1909.08320 by other authors; text overlap with arXiv:2007.09440, arXiv:1803.09287 by other authors