Twisted homology of quantum SL(2)

Hadfield, T. and Kraehmer, U. (2005) Twisted homology of quantum SL(2). K-Theory, 34(4), pp. 327-360. (doi: 10.1007/s10977-005-3118-2)

[img] Text


Publisher's URL:


We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators a,b,c,d. We discover a family of automorphisms for which the "twisted" Hochschild dimension coincides with the classical dimension of SL(2, C), thus avoiding the "dimension drop" in Hochschild homology seen for many quantum deformations. Strikingly, the simplest such automorphism is the canonical modular automorphism arising from the Haar functional. In addition, we identify the twisted cyclic cohomology classes corresponding to the three covariant differential calculi over quantum SU(2) discovered by Woronowicz.

Item Type:Articles
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:K-Theory
ISSN (Online):1573-0514

University Staff: Request a correction | Enlighten Editors: Update this record