The Hochschild Cohomology of a Poincaré Algebra

Second Hochschild Cohomology of Convolution Algebras

Poincaré Duality at the Chain Level, and a Bv Structure on the Homology of the Free Loops Space of a Simply Connected Poincaré Duality Space

We show that the simplicial chains, C•X, on a compact, triangulated, and oriented Poincaré duality space, X, of dimension d, can be endowed with an A∞ Poincaré duality structure. Using this, we show that the shifted Hochschild cohomology, HH(CX, C•X)[d], of the cochain algebra, CX, with values in the chains, C•X, has a BV structure. This is achieved by using the A∞ Poincaré duality structure to...

On the Hochschild Cohomology of Tame Hecke Algebras

In this paper we are interested in Hochschild cohomology of finite-dimensional algebras; the main motivation is to generalize group cohomology to larger classes of algebras. If suitable finite generation holds, one can define support varieties of modules as introduced by [SS]. Furthermore, when the algebra is self-injective, many of the properties of group representations generalize to this set...

The Bv Algebra on Hochschild Cohomology Induced by Infinity Inner Products

Abstract. We define a BV-structure on the Hochschild-cohomology of a unital, associative algebra A with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomolog...

Hochschild Cohomology of Algebras of Quaternion Type, I: Generalized Quaternion Groups

In terms of generators and defining relations, a description is given of the Hochschild cohomology algebra for one of the series of local algebras of quaternion type. As a corollary, the Hochschild cohomology algebra is described for the group algebras of generalized quaternion groups over algebraically closed fields of characteristic 2. Introduction Let R be a finite-dimensional algebra over a...