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Graded C*-algebras, Graded K-theory, And Twisted P-graph C*-algebras

Journal Article


Abstract


  • We develop methods for computing graded K-theory of C*-algebras

    as defined in terms of Kasparov theory. We establish graded versions

    of Pimsner’s six-term exact sequences for graded Hilbert bimodules whose

    left action is injective and by compacts, and a graded Pimsner–Voiculescu sequence.

    We introduce the notion of a twisted P-graph C*-algebra and establish

    connections with graded C*-algebras. Specifically, we show how a functor

    from a P-graph into the group of order two determines a grading of the associated

    C*-algebra. We apply our graded version of Pimsner’s exact sequence to

    compute the graded K-theory of a graph C*-algebra carrying such a grading.

Publication Date


  • 2018

Citation


  • Kumjian, A., Pask, D. & Sims, A. (2018). Graded C*-algebras, Graded K-theory, And Twisted P-graph C*-algebras. Journal of Operator Theory, 80 (2), 295-348.

Scopus Eid


  • 2-s2.0-85058473898

Number Of Pages


  • 53

Start Page


  • 295

End Page


  • 348

Volume


  • 80

Issue


  • 2

Place Of Publication


  • Romania

Abstract


  • We develop methods for computing graded K-theory of C*-algebras

    as defined in terms of Kasparov theory. We establish graded versions

    of Pimsner’s six-term exact sequences for graded Hilbert bimodules whose

    left action is injective and by compacts, and a graded Pimsner–Voiculescu sequence.

    We introduce the notion of a twisted P-graph C*-algebra and establish

    connections with graded C*-algebras. Specifically, we show how a functor

    from a P-graph into the group of order two determines a grading of the associated

    C*-algebra. We apply our graded version of Pimsner’s exact sequence to

    compute the graded K-theory of a graph C*-algebra carrying such a grading.

Publication Date


  • 2018

Citation


  • Kumjian, A., Pask, D. & Sims, A. (2018). Graded C*-algebras, Graded K-theory, And Twisted P-graph C*-algebras. Journal of Operator Theory, 80 (2), 295-348.

Scopus Eid


  • 2-s2.0-85058473898

Number Of Pages


  • 53

Start Page


  • 295

End Page


  • 348

Volume


  • 80

Issue


  • 2

Place Of Publication


  • Romania