info:eu-repo/semantics/article
The Gerstenhaber structure on the Hochschild cohomology of a class of special biserial algebras
Fecha
2021-08Registro en:
Meinel, Joanna; Nguyen, Van C.; Pauwels, Bregje; Redondo, Maria Julia; Solotar, Andrea Leonor; The Gerstenhaber structure on the Hochschild cohomology of a class of special biserial algebras; Academic Press Inc Elsevier Science; Journal of Algebra; 580; 8-2021; 264-298
0021-8693
CONICET Digital
CONICET
Autor
Meinel, Joanna
Nguyen, Van C.
Pauwels, Bregje
Redondo, Maria Julia
Solotar, Andrea Leonor
Resumen
We determine the Gerstenhaber structure on the Hochschild cohomology 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 nas a module over this Lie algebra by providing its decomposition as a direct sum of indecomposable modules.