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Twisted cyclic theory, equivariant KK-theory and KMS states

Journal Article


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Abstract


  • Given a C-algebra A with a KMS weight for a circle action, we construct

    and compute a secondary invariant on the equivariant K-theory of the mapping cone of

    AT ,! A, both in terms of equivariant KK-theory and in terms of a semifinite spectral

    flow. This in particular puts the previously considered examples of Cuntz algebras [10]

    and SUqð2Þ [14] in a general framework. As a new example we consider the Araki–Woods

    IIIl representations of the Fermion algebra.

Publication Date


  • 2011

Citation


  • Carey, A. L., Neshveyev, S., Nest, R. & Rennie, A. (2011). Twisted cyclic theory, equivariant KK-theory and KMS states. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal, 2011 (650), 161-191.

Scopus Eid


  • 2-s2.0-79551637145

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1741&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/735

Number Of Pages


  • 30

Start Page


  • 161

End Page


  • 191

Volume


  • 2011

Issue


  • 650

Abstract


  • Given a C-algebra A with a KMS weight for a circle action, we construct

    and compute a secondary invariant on the equivariant K-theory of the mapping cone of

    AT ,! A, both in terms of equivariant KK-theory and in terms of a semifinite spectral

    flow. This in particular puts the previously considered examples of Cuntz algebras [10]

    and SUqð2Þ [14] in a general framework. As a new example we consider the Araki–Woods

    IIIl representations of the Fermion algebra.

Publication Date


  • 2011

Citation


  • Carey, A. L., Neshveyev, S., Nest, R. & Rennie, A. (2011). Twisted cyclic theory, equivariant KK-theory and KMS states. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal, 2011 (650), 161-191.

Scopus Eid


  • 2-s2.0-79551637145

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1741&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/735

Number Of Pages


  • 30

Start Page


  • 161

End Page


  • 191

Volume


  • 2011

Issue


  • 650