The Hochschild cohomology of square-free monomial complete intersections

Abstract

We determine the Hochschild cohomology algebras of the square-free monomial complete intersections. In particular we provide a formula for the cup product which gives the cohomology module an algebra structure and then we provide a description of this structure in terms of generators and relations. In addition, we compute the Hilbert series of the Hochschild cohomology of these algebras.2010 Mathematics Subject Classification. 13D03.

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

“…Of particular interest to us are cases of algebras with more variables; however, the method in [1] can only work in case of algebras with one variable. In [2], the authors provided a concrete approach to deal with computing the Hochschild cohomology ring of square-free monomial complete intersections in n variables. The aim of this article is to obtain a description of the Hochschild cohomology ring of the numerical semigroup algebras k[s a , s b ] ⊆ k[s] of embedding dimension two, a case of non-monomial complete intersections in more than one variable.…”