The Gerstenhaber bracket and cycles in the module category of a monomial quadratic algebra

TL;DR

This paper explores the relationship between the Gerstenhaber bracket in Hochschild cohomology and the behavior of cycles within the module category of monomial quadratic algebras, revealing new structural insights.

Contribution

It establishes a novel connection between Hochschild cohomology structures and module category cycles in monomial quadratic algebras.

Findings

Link established between Gerstenhaber bracket and module cycles

Structural insights into monomial quadratic algebra modules

Potential implications for algebraic deformation theory

Abstract

We establish a link between the Gerstenhaber bracket in the Hochshild cohomology and the behaviour of cycles in the module category of a monomial quadratic algebra $A$.