Using non-commutative differential forms, we construct a complex called singular
Hochschild cochain complex for any associative algebra over a field. The cohomology of this …

We prove that, as Gerstenhaber algebras, the Hochschild cohomology ring of the tensor
product of two algebras is isomorphic to the tensor product of the respective Hochschild …

Given a differential graded (dg) symmetric Frobenius algebra A we construct an unbounded
complex D. A; A/, called the Tate–Hochschild complex, which arises as a totalization of a …

We prove formulas of different types that allow us to calculate the Gerstenhaber bracket on
the Hochschild cohomology of an algebra using some arbitrary projective bimodule …

Let $ X $ be a compact, oriented, second countable pseudomanifold. We show that $
HH^\ast_\bullet (\widetilde N^\ast_\bullet (X;\mathbb {Q})) $, the Hochschild cohomology of …

Keller proved in 1999 that the Gerstenhaber algebra structure on the Hochschild
cohomology of an algebra is an invariant of the derived category. In this paper, we adapt his …

Derived equivalences and stable equivalences of Morita type, and new (candidate)
invariants thereof, between symmetric algebras will be investigated, using transfer maps as …

Generalizing a conjecture of Deligne, Kontsevich proposed that there should be a notion of
Hochschild cohomology of algebras over the little cube operad (or its chain complex) which …

In this paper, we define the singular Hochschild cohomology groups $ HH_ {sg}^ i (A, A) $ of
an associative $ k $-algebra $ A $ as morphisms from $ A $ to $ A [i] $ in the singular …

The solution of Deligne's conjecture on Hochschild cochains and the formality of the operad
of little disks provide us with a natural homotopy Gerstenhaber algebra structure on the …