Dyer–Lashof–Cohen operations in Hochschild cohomology

Dyer-Lashof-Cohen operations in Hochschild cohomology

In the paper we give explicit formulae for operations in Hochschild cohomology which are analogous to the operations in the homology of double loop spaces. As a corollary we obtain that any brace algebra in finite characteristics is always a restricted Lie algebra.

Crossed Interval Groups and Operations on the Hochschild Cohomology

We introduce crossed interval groups and construct a crossed interval analog IS of the Fiedorowicz-Loday symmetric category ∆S. We prove that the functor FS(−) of the free IS-extension of an I-object does not change homotopy type. We then observe that the operad B of natural operations on the Hochschild cohomology equals FS(T ), where T is an operad whose homotopy type is known. We conclude fro...

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