Hochschild cohomology of socle deformations of a class of Koszul self-injective algebras

We consider the socle deformations arising from formal deformations of a class of Koszul self-injective special biserial algebras which occur in the study of the Drinfeld double of the generalized Taft algebras. We show, for these deformations, that the Hochschild cohomology ring modulo nilpotence is a finitely generated commutative algebra of Krull dimension 2.

💡 Research Summary

The paper investigates the Hochschild cohomology of a family of Koszul self‑injective special biserial algebras that arise in the study of the Drinfeld double of generalized Taft algebras. These algebras, denoted by (A), are known to be Koszul, self‑injective, and to possess a particularly tractable quiver presentation with binomial relations. The authors focus on a specific class of deformations obtained by altering the socle of (A) through formal deformation theory. Concretely, a formal parameter (t) is introduced and the socle idempotents are perturbed by a bimodule map (\delta), producing a family (A_t) of algebras over the power‑series ring (k