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arXiv · 1803.10909

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

Joanna Meinel·Van C. Nguyen·Bregje Pauwels·Maria Julia Redondo·Andrea Solotar
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Abstract

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 $n$ as a module over this Lie algebra by providing its decomposition as a direct sum of indecomposable modules.

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Joanna Meinel, Van C. Nguyen, Bregje Pauwels, Maria Julia Redondo, Andrea Solotar. 2018-03-29. The Gerstenhaber structure on the Hochschild cohomology of a class of special biserial algebras. https://arxiv.org/abs/1803.10909

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