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Spectral flow invariants and twisted cyclic theory for the Haar state on SUq(2)

Journal Article


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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 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 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 non-trivial `eta' contributions to this index.

Publication Date


  • 2009

Citation


  • Carey, A. L., Rennie, A. & Tong, K. (2009). Spectral flow invariants and twisted cyclic theory for the Haar state on SUq(2). Journal of Geometry and Physics, 59 1431-1452.

Scopus Eid


  • 2-s2.0-69249230783

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1697&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/691

Number Of Pages


  • 21

Start Page


  • 1431

End Page


  • 1452

Volume


  • 59

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 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 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 non-trivial `eta' contributions to this index.

Publication Date


  • 2009

Citation


  • Carey, A. L., Rennie, A. & Tong, K. (2009). Spectral flow invariants and twisted cyclic theory for the Haar state on SUq(2). Journal of Geometry and Physics, 59 1431-1452.

Scopus Eid


  • 2-s2.0-69249230783

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1697&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/691

Number Of Pages


  • 21

Start Page


  • 1431

End Page


  • 1452

Volume


  • 59