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

Mathematics – Rings and Algebras

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Some changes to section 5, to accommodate more precise version of Proposition 5.1. Other typos fixed

Scientific paper

We show that many noetherian Hopf algebras A have a rigid dualising complex R with R isomorphic to ^{\nu}A^1 [d]. Here, d is the injective dimension of the algebra and \nu 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 \nu the Nakayama automorphism of A. We prove that \nu = S^2\XXi, where S is the antipode of A and \XXi is the left winding automorphism of A determined by the left integral of A. The Hochschild homology and cohomology groups with coefficients in a suitably twisted free bimodule are shown to be non-zero in the top dimension d, when A is an Artin-Schelter regular noetherian Hopf algebra of global dimension d. (Twisted) Poincare duality holds in this setting, as is deduced from a theorem of Van den Bergh. Calculating \nu for A using also the opposite coalgebra structure, we determine a formula for S^4 generalising a 1976 formula of Radford for A finite dimensional. Applications of the results to the cases where A is PI, an enveloping algebra, a quantum group, a quantised function algebra and a group algebra are outlined.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-332555

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.