Generalized parallel paths method for computing the first Hochschild cohomology group with applications to Brauer graph algebras

TL;DR

This paper introduces a generalized parallel paths method using algebraic Morse theory to compute the first Hochschild cohomology groups, with applications to understanding Lie structures in Brauer graph algebras.

Contribution

It extends the parallel paths method via algebraic Morse theory for Hochschild cohomology calculations, specifically applied to Brauer graph algebras.

Findings

Describes the Lie structures of Hochschild cohomology groups

Provides a comparison between Brauer graph algebras and their graded counterparts

Advances computational techniques for Hochschild cohomology

Abstract

We use algebraic Morse theory to generalize the parallel paths method for computing the first Hochschild cohomology groups. As an application, we describe and compare the Lie structures of the first Hochschild cohomology groups of Brauer graph algebras and their associated graded algebras.