Estructura de álgebra de Gerstenhaber de la cohomología de Hochschild de una clase de álgebras biseriales

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

La Plata

Congreso; Reunión Anual Unión Matemática Argentina; 2018

Unión Matemática Argentina

We determine the Gerstenhaber structure on the Hochschild cohomology ring ofa class of self-injective special biserial algebras. Each of these algebras ispresented 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 ofcopies of a subquotient of the Virasoro algebra. These copies share Virasorodegree 0 and commute otherwise. Finally, we describe the cohomology in degree n as a module over this Lie algebra by providing its decomposition as adirect sum of indecomposable modules