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

Authors

Alexander Kumjian, University of NevadaFollow
David Pask, University of WollongongFollow
Aidan Sims, University of WollongongFollow

RIS ID

131593

Publication Details

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.

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.

Grant Number

ARC/DP150101598