The Hochschild Cohomology ring of preprojective algebras of type Ln

TL;DR

This paper computes the Hochschild cohomology ring of preprojective algebras of type Ln, providing an explicit presentation of its structure over fields with characteristic not 2.

Contribution

It offers the first explicit description of the Hochschild cohomology ring structure for these algebras, including generators and relations.

Findings

Hochschild cohomology ring computed explicitly

Ring structure described by generators and relations

Applicable over fields with characteristic not 2

Abstract

We compute the Hochschild Cohomology of a finite-dimensional preprojective algebra of generalized Dynkin type Ln over a field of characteristic different from 2 . In particular, we describe the ring structure of the Hochschild Cohomology ring under the Yoneda product by giving an explicit presentation by generators and relations.