The Hochschild cohomology ring of the numerical semigroup algebras of embedding dimension two

Abstract

Let $a$ and $b$ be two coprime positive integers and $k$ an arbitrary field. We determine the ring structure of the Hochschild cohomology of the numerical semigroup algebras $k[s^a,s^b]$ of embedding dimension two (thus also complete intersections) in terms of generators and relations. In addition, we compute the Hilbert series for this cohomology ring.

19 pages