Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras

Dualising Complexes and Twisted Hochschild (co)homology for Noetherian Hopf Algebras

We show that many noetherian Hopf algebras A have a rigid dualising complex R with R = A[d]. Here, d is the injective dimension of the algebra and ν is a certain k-algebra automorphism of A, unique up to an inner automorphism. In honour of the finite dimensional theory which is hereby generalised we call ν the Nakayama automorphism of A. We prove that ν = Sξ, where S is the antipode of A and ξ ...

Hochschild Cohomology of Smash Products and Rank One Hopf Algebras

We give some general results on the ring structure of Hochschild cohomology of smash products of algebras with Hopf algebras. We compute this ring structure explicitly for a large class of finite dimensional Hopf algebras of rank one.

Noetherian Hopf Algebras

This short survey article reviews our current state of understanding of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed. To the memory of my teacher and friend Brian Hartley

Hochschild Cohomology for Complex Spaces and Noetherian Schemes

The classical HKR-theorem gives an isomorphism of the n-th Hochschild cohomology of a smooth algebra and the n-th exterior power of its module of Kähler differentials. Here we generalize it for simplicial, graded and anticommutative objects in “good pairs of categories”. We apply this generalization to complex spaces and noetherian schemes and deduce two decomposition theorems for their (relati...

Second Hochschild Cohomology of Convolution Algebras