This article is based on the author’s talk at international conference dedicated to memory of Professor B. Yu. Sternin (Moscow, November 6–9, 2018). The Hochschild homology and cohomology a group algebra can be described via classifying space adjoint action groupoid under suitable assumption finiteness supports groups. difference between leads correction results in D. J. Benson’s book Represent...

In this work we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The is universal envelope Virasoro Lie relative to locality $N=2$. order obtain result adjust algebraic discrete Morse theory case differential algebras.

We compare two different types of mapping class invariants: the Hochschild homology an A∞ bimodule coming from bordered Heegaard Floer and fixed point cohomology. first compute invariants their in genus case. then resulting computations to cohomology make a conjecture that are isomorphic. also discuss construction map potentially giving isomorphism. It comes as open-closed context surface viewe...

In this paper we study sufficient conditions for the solvability of first Hochschild cohomology a finite dimensional algebra as Lie in terms its Ext-quiver arbitrary characteristic. particular, show that if quiver has no parallel arrows and loops then is solvable. For quivers containing loops, determine easily verifiable cohomology. We apply these criteria to space large families algebras, name...

As Don Schack mentioned in his plenary talk [SDS], Gerstenhaber [MG] observed that if A is an associative algebra, then the Hochschild cohomology of A is a graded commutative algebra with an additional structure, viz., that of a Lie algebra. The two structures satisfy a compatibility condition (graded Poission structure). We agree to call such structures G–algebras (Gerstenhaber–algebras). Scha...