Hochschild cohomology for self-injective algebras of tree class $D_n$. I

The minimal projective bimodule resolution is constructed for algebras in a family of selfinjective algebras of finite representation type and with tree class $D_n$. Using this resolution we calculate dimensions of the Hochschild cohomology groups for the algebras under consideration. The described resolution is periodic, and hence, the Hochschild cohomology of these algebras is periodic too.