Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras

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This paper presents, by example, an index theory appropriate to algebras without trace. Whilst we work exclusively with the Cuntz algebras the exposition is designed to indicate how to develop a general theory. Our main result is an index theorem (formulated in terms of spectral flow) using a twisted cyclic cocycle where the twisting comes from the modular automorphism group for the canonical gauge action on the Cuntz algebra. We introduce a modified $K_1$-group of the Cuntz algebra so as to pair with this twisted cocycle. As a corollary we obtain a noncommutative geometry interpretation for Araki's notion of relative entropy in this example. We also note the connection of this example to the theory of noncommutative manifolds.
27 pages, minor corrections

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K-Theory and Homology, Operator Algebras, 46L80

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http://salesiana.dossiersoluciones.com/handle/123456789/155830

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0801.4605
 http://arxiv.org/abs/0801.4605

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arXiv