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

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dc.creatorCarey, A. L.
dc.creatorPhillips, J.
dc.creatorRennie, A.
dc.date2008-01-30
dc.date2008-02-29
dc.date.accessioned2026-07-07T09:23:42Z
dc.date.available2026-07-07T09:23:42Z
dc.descriptionThis 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.
dc.description27 pages, minor corrections
dc.identifierhttps://arxiv.org/abs/0801.4605
dc.identifierhttp://arxiv.org/abs/0801.4605
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155830
dc.subjectK-Theory and Homology
dc.subjectOperator Algebras
dc.subject46L80
dc.titleTwisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras
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