Gerstenhaber structure of a class of special biserial algebras

ANDREA SOLOTAR

Trieste

Conferencia; ICTP Math Seminar; 2018

International Centre for Theoretical Physics

We consider a class of self-injective special biserialalgebras presented as the quotient of a path algebra over a eld k of a quiver Q with m vertices and 2m arrows by an ideal generated by 3m relations. We study the Gerstenhaber structure of its Hochschild cohomology ring. It has been proved by Snashall and Taillefer that this Hochschild cohomology ring is a nitely generated k-algebra. We employ their cohomology computations and Suarez- Alvarez's approach, which in this case afford the complete computation of Gerstenhaber brackets in cohomology. Furthermore, we study the Lie algebra structure of the degree-1 cohomology, which consists of m copies of a quotient of a subalgebra of the Virasoro algebra that share Virasoro degree 0 and that commute otherwise. We provide a decomposition of each space cohomology space as a module over the first cohomology space.