A Hochschild cohomology comparison theorem for prestacks

A Hochschild Cohomology Comparison Theorem for Prestacks

We generalize and clarify Gerstenhaber and Schack’s “Special Cohomology Comparison Theorem”. More specifically we obtain a fully faithful functor between the derived categories of bimodules over a prestack over a small category U and the derived category of bimodules over its corresponding fibered category. In contrast to Gerstenhaber and Schack we do not have to assume that U is a poset.

The Atiyah class, Hochschild cohomology and the Riemann–Roch theorem

The present paper grew up from a question posed to the author by B. Feigin: ”Why does the Todd class look like the invariant volume form on a Lie group?” The answer is in a sense contained in the proof of proposition 6. In the first part we develop a formalism describing the Atiyah class, Hochschild cohomology and homology and relations between them. Essentially we introduce a global analog of ...

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