A family of Koszul self-injective algebras with finite Hochschild cohomology

Abstract

This paper presents an infinite family of Koszul self-injective algebras whose Hochschild cohomology ring is finite-dimensional. Moreover, for each N ⩾ 5 we give an example where the Hochschild cohomology ring has dimension N . This family of algebras includes and generalizes the 4-dimensional Koszul self-injective local algebras of [R.-O. Buchweitz, E.L. Green, D. Madsen, Ø. Solberg, Finite Hochschild cohomology without finite global dimension, Math. Res. Lett. 12 (2005) 805–816] which were used to give a negative answer to Happel’s question, in that they have infinite global dimension but finite-dimensional Hochschild cohomology.