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

作者：Parker Alison; Snashall Nicole^*

来源：Journal of Pure and Applied Algebra, 2012, 216(5): 1245-1252.

DOI：10.1016/j.jpaa.2011.12.011

This paper presents an infinite family of Koszul self-injective algebras whose Hochschild cohomology ring is finite-dimensional. Moreover, for each N %26gt;= 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, O. Solberg, Finite Hochschild cohomology without finite global dimension, Math. Res. Lett. 12 (2005) 805-816] which were used to give a negative answer to Flappers question, in that they have infinite global dimension but finite-dimensional Hochschild cohomology.

• 出版日期2012-5