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Gerstenhaber structure of a class of special biserial algebras

Andrea Solotar
Universidad de Buenos Aires
Luigi Stasi Seminar Room, ICTP
Thursday, February 8, 2018 - 14:00

For any integer N≥1, we consider a class of self-injective special biserial algebras AN given by quiver and relations over a field k. We study the Gerstenhaber structure of its Hochschild cohomology ring HH∗(AN). This Hochschild cohomology ring is a finitely generated k-algebra, due to the results by Snashall and Taillefer. We employ their cohomology computations and Suárez-Álvarez’s approach to compute all Gerstenhaber brackets of HH∗(AN). Furthermore, we study the Lie algebra structure of the degree-1 cohomology HH1(AN ) as embedded into a direct sum of Virasoro algebras and provide a decomposition of HHn(AN ) as a module over HH1(AN ).

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