On the Hochschild homology of quantum SL(N)

Hadfield, T. and Kraehmer, U. (2006) On the Hochschild homology of quantum SL(N). Comptes Rendus Mathématique, 343(1), pp. 9-13. (doi: 10.1016/j.crma.2006.03.031)

Abstract

We show that the quantized coordinate ring A:=kq[SL(N)] satisfies van den Bergh's analogue of Poincaré duality for Hochschild (co)homology with dualizing bimodule being Aσ, the A-bimodule which is A as k-vector space with right multiplication twisted by the modular automorphism σ of the Haar functional. This implies that HN2−1(A,Aσ)≅ congruent withk, generalizing our previous result for kq[SL(2)].

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kraehmer, Dr Ulrich
• Authors: Hadfield, T., and Kraehmer, U.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Comptes Rendus Mathématique
• ISSN: 1631-073X