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arXiv · 1706.00563

Graded C*-algebras, graded K-theory, and twisted P-graph C*-algebras

Alex Kumjian·David Pask·Aidan Sims
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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 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.

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Alex Kumjian, David Pask, Aidan Sims. 2017-06-02. Graded C*-algebras, graded K-theory, and twisted P-graph C*-algebras. https://arxiv.org/abs/1706.00563

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