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

@article{Kumjian2017GradedCG, title={Graded C*-algebras, Graded K-theory, And Twisted P-graph C*-algebras}, author={Alex Kumjian and David Pask and Aidan Sims}, journal={arXiv: Operator Algebras}, year={2017}, pages={295} }

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…

## 6 Citations

### Graded K-theory and K-homology of relative Cuntz–Pimsner algebras and graph C⁎-algebras

- MathematicsJournal of Mathematical Analysis and Applications
- 2021

### Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras

- MathematicsIndiana University Mathematics Journal
- 2022

We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have isomorphic K-theory. As an application, we give a…

### The Cayley transform in complex, real and graded K-theory

- Mathematics
- 2019

We use the Cayley transform to provide an explicit isomorphism at the level of cycles from van Daele $K$-theory to $KK$-theory for graded $C^*$-algebras with a real structure. Isomorphisms between…

### Honours thesis: Exact sequences in graded $KK$-theory for Cuntz-Pimsner algebras

- Mathematics
- 2020

In this thesis we generalise the six-term exact sequence in graded $KK$-theory obtained in a paper of Kumjian, Pask and Sims (2017) to allow correspondences with non-compact left action. In…

### K-theory and homotopies of twists on ample groupoids

- MathematicsJournal of Noncommutative Geometry
- 2021

This paper investigates the K-theory of twisted groupoid C*-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum–Connes conjecture with coefficients gives rise to…

### $\mathrm{K}$-theory and homotopies of twists on ample groupoids

- Mathematics
- 2019

This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with…

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