Hochschild cohomology for periodic algebras of polynomial growth

TL;DR

This paper investigates the Hochschild cohomology dimensions of specific periodic algebras with polynomial growth, revealing their structural properties and relationships to other algebra classes.

Contribution

It provides a detailed description of Hochschild cohomology for exceptional periodic algebras of polynomial growth and distinguishes their derived equivalence classes.

Findings

Hochschild cohomology dimensions are explicitly described for these algebras.

Non-standard periodic algebras of polynomial growth are not derived equivalent to standard self-injective algebras.

Abstract

We describe the dimensions of low Hochschild cohomology spaces of exceptional periodic representation-infinite algebras of polynomial growth. As an application we obtain that an indecomposable non-standard periodic representation-infinite algebra of polynomial growth is not derived equivalent to a standard self-injective algebra.