Abstract
We consider a class of self-injective special biserial algebras ΛN over a field K and show that the Hochschild cohomology ring of dΛN is a finitely generated K-algebra. Moreover, the Hochschild cohomology ring of ΛN modulo nilpotence is a finitely generated commutative K-algebra of Krull dimension two. As a consequence the conjecture of [N. Snashall and Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc.88 (2004) 705–732], concerning the Hochschild cohomology ring modulo nilpotence, holds for this class of algebras.
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