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

Abstract

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.

25 pages, 1 figure

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Cited by in corpus (8)

• Twisted cyclic theory, equivariant KK theory and KMS States
• A modular spectral triple for $\kappa$-Minkowski space
• Modular Theory, Non-Commutative Geometry and Quantum Gravity
• Modular Index Invariants of Mumford Curves
• Constructing KMS states from infinite-dimensional spectral triples
• On modular semifinite index theory
• Quantum Dimension and Quantum Projective Spaces
• Non-commutative integration, zeta functions and the Haar state for $S{U}_q(2)$