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

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.