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 $N\ge 5$ 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 Buchweitz, Green, Madsen and Solberg, which were used to give a negative answer to Happel's question, in that they have infinite global dimension but finite-dimensional Hochschild cohomology.

17 pages

References in corpus (2)

• Resolutions over Koszul algebras
• Representation theory of liftings of quantum planes