Hochschild cohomology of graded skew-gentle algebras: Gerstenhaber algebra structure and geometric interpretation

TL;DR

This paper computes the Hochschild cohomology of graded skew-gentle algebras, revealing its algebraic and geometric structures and linking it to the topology of underlying graded surfaces.

Contribution

It provides explicit calculations of Hochschild cohomology and its Gerstenhaber algebra structure for graded skew-gentle algebras, connecting algebraic invariants to geometric surfaces.

Findings

Hochschild cohomology is a graded commutative algebra with a Lie algebra structure.

Hochschild cohomology encodes information about the underlying graded surface.

Results apply to partially wrapped Fukaya categories of orbifold surfaces.

Abstract

In this paper we calculate the Hochschild cohomology of graded skew-gentle algebras, together with its structure as graded commutative algebra under the cup product and its Lie algebra structure given by the Gerstenhaber bracket. One of the results of this paper is that for graded skew-gentle algebras and thus also for partially wrapped Fukaya categories of orbifold surfaces with stops, their Hochschild cohomology is encoded in the underlying graded surface.