Graded C*-algebras, graded K-theory, and twisted P-graph C*-algebras
Alex Kumjian, David Pask, Aidan Sims

TL;DR
This paper develops methods for computing graded K-theory of C*-algebras, introduces twisted P-graph C*-algebras, and establishes graded versions of Pimsner's sequences, advancing the understanding of graded structures in operator algebras.
Contribution
It introduces graded versions of Pimsner's sequences, defines twisted P-graph C*-algebras, and applies these tools to compute graded K-theory of graph C*-algebras.
Findings
Established graded Pimsner six-term sequences.
Defined twisted P-graph C*-algebras and their gradings.
Computed graded K-theory for specific graph C*-algebras.
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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Taxonomy
TopicsAdvanced Operator Algebra Research
