Abstract

In [A.L. Carey, J. Phillips, A. Rennie, Twisted cyclic theory and an index theory for the
gauge invariant KMS state on Cuntz algebras. arXiv:0801.4605], we presented a Ktheoretic
approach to finding invariants of algebras with no nontrivial 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 nonfaithful traces, namely SUq.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 [A.L. Carey,
J. Phillips, A. Rennie, Twisted cyclic theory and an index theory for the gauge invariant
KMS state on Cuntz algebras. arXiv:0801.4605], the computations are considerably more
complex and interesting, because there are nontrivial `eta' contributions to this index.