We investigate Hochschild cohomology and homology of admissible subcategories of derived categories of coherent sheaves on smooth projective varieties. We show that the Hochschild cohomology of an admissible subcategory is isomorphic to the derived endomorphisms of the kernel giving the corresponding projection functor, and the Hochschild homology is isomorphic to derived morphisms from this ke...

We show that the continuous Hochschild cohomology and the differential Hochschild cohomology of the Hida test algebra endowed with the normalized Wick product are the same.

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...

The classical HKR-theorem gives an isomorphism of the n-th Hochschild cohomology of a smooth algebra and the n-th exterior power of its module of Kähler differentials. Here we generalize it for simplicial, graded and anticommutative objects in “good pairs of categories”. We apply this generalization to complex spaces and noetherian schemes and deduce two decomposition theorems for their (relati...

We construct the Gerstenhaber bracket on Hochschild cohomology of a twisted tensor product of algebras, and, as examples, compute Gerstenhaber brackets for some quantum complete intersections arising in work of Buchweitz, Green, Madsen, and Solberg. We prove that a subalgebra of the Hochschild cohomology ring of a twisted tensor product, on which the twisting is trivial, is isomorphic, as a Ger...

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...

We study the Lie module structure given by the Gerstenhaber bracket on the Hochschild cohomology groups of a monomial algebra with radical square zero. The description of such Lie module structure will be given in terms of the combinatorics of the quiver. The Lie module structure will be related to the classification of finite dimensional modules over simple Lie algebras when the quiver is give...

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...

We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We then show that the Hochschild cohomology ring modulo nilpotence is a finitely generated algebra of Krull dimension 2, and describe the support varieties of modules for these algebras.