Gerstenhaber Algebra Structure on the Hochschild Cohomology of Quadratic String Algebras

REDONDO, MARÍA JULIA; ROMÁN, LUCRECIA

Algebras and Representation Theory

SPRINGER

Año: 2018 vol. 21 p. 61 - 86

1386-923X

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