On Kontsevich's Hochschild cohomology conjecture

On Kontsevich’s Hochschild cohomology conjecture

A Solution of Deligne's Hochschild Cohomology Conjecture

Deligne asked in 1993 whether the Hochschild cochain complex of an associative ring has a natural action by the singular chains of the little 2-cubes operad. In this paper we give an affirmative answer to this question. We also show that the topological Hochschild cohomology spectrum of an associative ring spectrum has an action by an operad that is equivalent to the little 2-cubes operad.

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...

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...

Second Hochschild Cohomology of Convolution Algebras