Hochschild Homology and Cohomology of Klein Surfaces

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...

Hochschild Homology and Semiorthogonal Decompositions

We investigate Hochschild cohomology and homology of admissible subcategories of derived categories of coherent sheaves on smooth projective varieties. We show that the Hochschild cohomology of an admissible subcategory is isomorphic to the derived endomorphisms of the kernel giving the corresponding projection functor, and the Hochschild homology is isomorphic to derived morphisms from this ke...

Second Hochschild Cohomology of Convolution Algebras

Hochschild Homology and Split Pairs

We study the Hochschild homology of algebras related via split pairs, and apply this to fibre products, trivial extensions, monomial algebras, graded-commutative algebras and quantum complete intersections. In particular, we compute lower bounds for the dimensions of both the Hochschild homology and cohomology groups of quantum complete intersections.

Hochschild (co)homology of exterior algebras

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generat...