The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content

NCG

Seminar

On the Hochschild homology of quantum groups

Kraehmer, U (Polish Academy of Sciences)
Wednesday 02 August 2006, 10:00-11:00

Seminar Room 1, Newton Institute

Abstract

This talk reports on two papers written in collaboration with T.Hadfield. In the first we computed the Hochschild homology of the standard quantisation of SL(2) with coefficients in bimodules obtained from the algebra itself by twisting the multiplication on one side by an automorphism. It turned out that precisely for Woronowicz's modular automorphism there is a unique nontrivial Hochschild class in degree 3=dim(SL(2)), in contrast to the untwisted case where all homologies were known to vanish in degrees greater than one. In the second paper we generalised this to SL(N) by showing that the quantisations satisfy van den Bergh's analogue of Poincare duality in Hochschild (co)homology. This was extended recently by K.Brown and J.Zhang to all Noetherian Artin-Schelter Gorenstein Hopf algebras. These results clarify the purely homological relevance of the twisted coefficients whose study was originally motivated by their relation to the theory of covariant differential calculi over quantum groups.

Presentation

[dvi ]

Audio

MP3MP3 Real AudioReal Audio

Back to top ∧