The Hochschild cohomology of square-free monomial complete intersections

TL;DR

This paper computes the Hochschild cohomology algebras of square-free monomial complete intersections, providing explicit formulas for the algebra structure, generators, relations, and Hilbert series.

Contribution

It offers the first explicit description of the Hochschild cohomology algebra structure for this class of algebras, including formulas and generators.

Findings

Derived a formula for the cup product in Hochschild cohomology

Described the algebra structure in terms of generators and relations

Computed the Hilbert series of the Hochschild cohomology

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 describe this structure in terms of generators and relations. In addition, we compute the Hilbert series of the Hochschild cohomology of these algebras.