Twisted cyclic theory, equivariant KK-theory and KMS states

By Alan L. Carey, Sergey Neshveyev, R. Nest, A. Rennie. 2008

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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 , 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 SU q (2) [Carey, Rennie, Tong, J. Geom. Phys. 59: 1431–1452, 2009] in a general framework. As a new example we consider the Araki–Woods III λ representations of the Fermion algebra.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d6dbba97ca9455f6752ece08bc7908ef2315adb6