Mathematics > Quantum Algebra
[Submitted on 13 May 2004 (v1), last revised 27 Jun 2005 (this version, v5)]
Title:Twisted homology of quantum SL(2)
View PDFAbstract: 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.
Submission history
From: Tom Hadfield [view email][v1] Thu, 13 May 2004 11:49:21 UTC (15 KB)
[v2] Sat, 19 Jun 2004 14:08:16 UTC (15 KB)
[v3] Fri, 2 Jul 2004 14:52:32 UTC (18 KB)
[v4] Fri, 3 Dec 2004 16:02:34 UTC (22 KB)
[v5] Mon, 27 Jun 2005 13:08:33 UTC (28 KB)
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