Distinguishing derived equivalence classes using the second Hochschild cohomology group

Abstract

In this paper we study the second Hochschild cohomology group of the preprojective algebra of type $D_4$ over an algebraically closed field $K$ of characteristic 2. We also calculate the second Hochschild cohomology group of a non-standard algebra which arises as a socle deformation of this preprojective algebra and so show that the two algebras are not derived equivalent. This answers a question raised by Holm and Skowroński.