The Hochschild cohomology ring of a class of special biserial algebras

Details The Hochschild cohomology ring of a class of special biserial algebras The Hochschild cohomology ring of a class of special biserial algebras

2008-03-11

arxiv.org/abs/0803.1536v1

Mathematics

Rings and Algebras

Scientific paper

We consider a class of self-injective special biserial algebras $\Lambda_N$ over a field $K$ and show that the Hochschild cohomology ring of $\Lambda_N$ is a finitely generated $K$-algebra. Moreover the Hochschild cohomology ring of $\Lambda_N$ modulo nilpotence is a finitely generated commutative $K$-algebra of Krull dimension two. As a consequence the conjecture of Snashall-Solberg \cite{SS}, concerning the Hochschild cohomology ring modulo nilpotence, holds for this class of algebras.

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