Twisted cyclic homology of all Podles quantum spheres

Details Twisted cyclic homology of all Podles quantum spheres Twisted cyclic homology of all Podles quantum spheres

2004-05-13

arxiv.org/abs/math/0405243v6

Journal of Geometry and Physics, 57, no. 2, 339-351 (2007)

Mathematics

Quantum Algebra

17 pages, no figures, uses the amscd package. v6: final version accepted for publication

Scientific paper

10.1016/j.geomphys.2006.03.006

We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of all Podles quantum spheres relative to arbitary automorphisms. Our calculations are based on a free resolution due to Masuda, Nakagami and Watanabe. The dimension drop in Hochschild homology can be overcome by twisting by automorphisms induced from the canonical modular automorphism associated to the Haar state on quantum SU(2). We specialize our results to the standard quantum sphere, and identify the class in twisted cyclic cohomology of the 2-cocycle discovered by Schmuedgen and Wagner corresponding to the distinguished covariant differential calculus found by Podles.

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