Hochschild Cohomology with Support

Higher order Hochschild cohomology

Following ideas of Pirashvili, we define higher order Hochschild cohomology over spheres S defined for any commutative algebra A and module M . When M = A, we prove that this cohomology is equipped with graded commutative algebra and degree d Lie algebra structures as well as with Adams operations. All operations are compatible in a suitable sense. These structures are related to Brane topology...

Hochschild Cohomology and Support Varieties for Tame Hecke Algebras

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.

Alternated Hochschild Cohomology

In this paper we construct a graded Lie algebra on the space of cochains on a Z2-graded vector space that are skew-symmetric in the odd variables. The Lie bracket is obtained from the classical Gerstenhaber bracket by (partial) skew-symmetrization; the coboundary operator is a skew-symmetrized version of the Hochschild differential. We show that an order-one element m satisfying the zero-square...

Hochschild Cohomology of Factors with Property Γ

The main result of this paper is that the kth continuous Hochschild cohomology groups Hk(M,M) and Hk(M, B(H)) of a von Neumann factor M ⊆ B(H) of type II1 with property Γ are zero for all positive integers k. The method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of Grothendieck type for multilinear maps. We prove joint continuity in...

Second Hochschild Cohomology of Convolution Algebras