Equivariant associative dialgebras and its one-parameter formal deformations

Associative dialgebras generalize the notions of associative algebras. In this paper, we define a notion of finite group actions on associative dialgebras and define an equivariant dialgebra cohomology associated with such actions. We introduce a one-parameter formal deformation in the equivariant context and show that the equivariant dialgebra cohomology controls the equivariant one-parameter formal deformation of dialgebra equipped with an action of a finite group.