The second Hochschild cohomology and deformations of Brauer graph algebras

TL;DR

This paper explicitly describes the second Hochschild cohomology of bipartite Brauer graph algebras and interprets related deformations geometrically via surface models.

Contribution

It provides a detailed computation of Hochschild cohomology and links algebraic deformations to geometric surface models for Brauer graph algebras.

Findings

Explicit description of second Hochschild cohomology groups.

Geometric interpretation of algebraic deformations.

Connection between cocycles and surface models.

Abstract

In this paper, we give an explicit description about the second Hochschild cohomology groups of bipartite Brauer graph algebras with trivial grading. Based on this, we provide geometric interpretations of deformations associated to some standard cocycles in terms of the surface models of Brauer graph algebras.