Gerstenhaber algebra structure on the Hochschild cohomology of quadratic string algebras

Abstract

We describe the Gerstenhaber algebra structure on the Hochschild cohomology HH*$(A)$ when $A$ is a quadratic string algebra. First we compute the Hochschild cohomology groups using Barzdell's resolution and we describe generators of these groups. Then we construct comparison morphisms between the bar resolution and Bardzell's resolution in order to get formulae for the cup product and the Lie bracket. We find conditions on the bound quiver associated to string algebras in order to get non-trivial structures.

arXiv commentFinal version to appear in Algebras and Representation Theory, 33 pages

References in corpus (6)

• Combinatorial derived invariants for gentle algebras
• Applications of the change-of-rings spectral sequence to the computation of Hochschild cohomology
• Hochschild cohomology via incidence algebras
• Hochschild cohomology of gentle algebras
• Gerstenhaber brackets on Hochschild cohomology of quantum symmetric algebras and their group extensions
• The Hochschild cohomology and the Tamarkin-Tsygan calculus of gentle algebras

Cited by in corpus (4)

• Polyvector fields for Fano 3-folds
• The Hochschild cohomology ring of monomial algebras
• The Gerstenhaber bracket and cycles in the module category of a monomial quadratic algebra
• Hochschild cohomology of $m$-Cluster tilted algebras of type $\tilde{\mathbb{A}}$