Hochschild Cohomology of Projective Hypersurfaces

Second Hochschild Cohomology of Convolution Algebras

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...

Hochschild Cohomology of Truncated Polynomials

The main result of this paper is to calculate the Batalin-Vilkovisky structure of HH∗(C∗(KPn;R);C∗(KPn;R)) for K = C andH, and R = Z and any field; and shows that in the special case when M = CP 1 = S2, and R = Z, this structure can not be identified with the BV-structure of H∗(LS 2;Z) computed by Luc Memichi in [16]. However, the induced Gerstenhaber structures are still identified in this cas...

Hochschild Cohomology of Cubic Surfaces

We consider the polynomial algebra C[z] := C[z1, z2, z3] and the polynomial f := z 3 1 + z 3 2 + z 3 3 + 3qz1z2z3, where q ∈ C. Our aim is to compute the Hochschild homology and cohomology of the cubic surface Xf := {z ∈ C 3 / f(z) = 0}. For explicit computations, we shall make use of a method suggested by M. Kontsevich. Then, we shall develop it in order to determine the Hochschild homology an...