Spectral flow invariants and twisted cyclic theory from the Haar state on SU_q(2)

Details Spectral flow invariants and twisted cyclic theory from the Haar state on SU_q(2) Spectral flow invariants and twisted cyclic theory from the Haar state on SU_q(2)

2008-02-04

arxiv.org/abs/0802.0317v1

Mathematics

Operator Algebras

25 pages, 1 figure

Scientific paper

In [CPR2], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only non-faithful traces, namely SU_q(2), and also KMS states. Our main results are index theorems (which calculate spectral flow), one using ordinary cyclic cohomology and the other using twisted cyclic cohomology, where the twisting comes from the generator of the modular group of the Haar state. In contrast to the Cuntz algebras studied in [CPR2], the computations are considerably more complex and interesting, because there are nontrivial `eta' contributions to this index.

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