The Hochschild cohomology groups under gluing arrows

TL;DR

This paper investigates how Hochschild cohomology groups of finite-dimensional monomial algebras change when two arrows are glued together, extending previous work on gluing idempotents.

Contribution

It introduces a comparison of Hochschild cohomology groups under the operation of gluing two arrows in monomial algebras, expanding the understanding of algebra modifications.

Findings

Hochschild cohomology groups are affected by arrow gluing.

Explicit descriptions of cohomology changes under arrow gluing.

Extension of previous idempotent gluing results to arrow gluing.

Abstract

In a previous paper arXiv:2211.05435 we have compared the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two idempotents. In the present paper, we compare the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two arrows.