The Gerstenhaber structure on the Hochschild cohomology of a class of special biserial algebras

MEINEL, JOANNA; NGUYEN, VAN; PAUWLES, BREGJE; REDONDO, MARIA JULIA; SOLOTAR, ANDREA

JOURNAL OF ALGEBRA

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2021 vol. 580 p. 264 - 298

0021-8693

We determine the Gerstenhaber structure on the Hochschild ring of a class of self-injective special biserial algebras. Each of these algebras is presented as a quotient of the path algebra of a certain quiver. In degree one, we show that the cohomology is isomorphic, as a Lie algebra, to a direct sum of copies of a subquotient of the Virasoro algebra. These copies share Virasoro degree 0 and commute otherwise. Finally, we describe the cohomology in degree n as a module over this Lie algebra by providing its decomposition as a direct sum of indecomposable modules.