On the Hochschild cohomology of truncated cycle algebras

The purpose of this paper is to study the Hochschild cohomology ring II . (Lambda) of algebras of the form Lambda = kZ(e) / J(N), where Z(e) is an oriented cycle with e vertices and J is the ideal generated by the arrows, N greater than or equal to 2. We provide a new description of the Yoneda product in H . (Lambda) and prove that this is a finitely generated infinite dimensional ring. In addition we show that algebras of the form Lambda = kZ(e)/J(N) are not derived equivalent unless they are isomorphic.