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Twisted cyclic theory, equivariant KK-theory and KMS states
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Alan L. Carey
,
Sergey Neshveyev
Published/Copyright:
January 7, 2011
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 
, 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 [Carey, Phillips, Rennie, Twisted cyclic theory and the modular index theory of Cuntz algebras] and SUq(2) [Carey, Rennie, Tong, J. Geom. Phys. 59: 1431–1452, 2009] in a general framework. As a new example we consider the Araki–Woods IIIλ representations of the Fermion algebra.
Received: 2009-02-03
Revised: 2009-05-01
Published Online: 2011-01-07
Published in Print: 2011-January
© Walter de Gruyter Berlin · New York 2011
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Articles in the same Issue
- Ricci soliton solvmanifolds
- Rational normal scrolls and the defining equations of Rees algebras
- Classifications of linear operators preserving elliptic, positive and non-negative polynomials
- Graded polynomial identities and exponential growth
- Un théorème de la masse positive pour le problème de Yamabe en dimension paire
- Degenerate problems with irregular obstacles
- Twisted cyclic theory, equivariant KK-theory and KMS states
- A trace formula for varieties over a discretely valued field
