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

A. L. Carey, J. Phillips, A. Rennie

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    Abstract

    This paper presents, by example, an index theory appropriate to algebras without trace. Whilst we work exclusively with 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 each Cuntz algebra. We introduce a modified K 1-group for each Cuntz algebra which has an index pairing with this twisted cocycle. This index pairing for Cuntz algebras has an interpretation in terms of Araki's notion of relative entropy.

    Original languageEnglish
    Pages (from-to)339-380
    Number of pages42
    JournalJournal of K-Theory
    Volume6
    Issue number2
    DOIs
    Publication statusPublished - 2010

    Fingerprint

    Dive into the research topics of 'Twisted cyclic theory and an index theory for the gauge invariant KMS state on the Cuntz algebra On'. Together they form a unique fingerprint.

    Cite this