Abstract
We calculate the 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 coincides with the classical 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 cyclic cohomology classes corresponding to the three covariant differential calculi over quantum SU(2) discovered by Woronowicz.
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