Twisted cyclic theory, equivariant KK theory and KMS States

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dc.creatorCarey, Alan L.
dc.creatorNeshveyev, Sergey
dc.creatorNest, Ryszard
dc.creatorRennie, Adam
dc.date2008-08-22
dc.date.accessioned2026-07-07T09:57:55Z
dc.date.available2026-07-07T09:57:55Z
dc.descriptionRecently, examples of an index theory for KMS states of circle actions were discovered, \cite{CPR2,CRT}. We show that these examples are not isolated. Rather there is a general framework in which we use KMS states for circle actions on a C*-algebra A to construct Kasparov modules and semifinite spectral triples. By using a residue construction analogous to that used in the semifinite local index formula we associate to these triples a twisted cyclic cocycle on a dense subalgebra of A. This cocycle pairs with the equivariant KK-theory of the mapping cone algebra for the inclusion of the fixed point algebra of the circle action in A. The pairing is expressed in terms of spectral flow between a pair of unbounded self adjoint operators that are Fredholm in the semifinite sense. A novel aspect of our work is the discovery of an eta cocycle that forms a part of our twisted residue cocycle. To illustrate our theorems we observe firstly that they incorporate the results in \cite{CPR2,CRT} as special cases. Next we use the Araki-Woods III_λrepresentations of the Fermion algebra to show that there are examples which are not Cuntz-Krieger systems.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/0808.3029
dc.identifierhttp://arxiv.org/abs/0808.3029
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167522
dc.subjectOperator Algebras
dc.subjectK-Theory and Homology
dc.titleTwisted cyclic theory, equivariant KK theory and KMS States
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