On the K-theory of twisted higher-rank-graph C*-algebras

@article{Kumjian2012OnTK,
  title={On the K-theory of twisted higher-rank-graph C*-algebras},
  author={Alex Kumjian and David Pask and Aidan Sims},
  journal={arXiv: Operator Algebras},
  year={2012}
}
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24 Citations
Highly Influential Citations
1
Background Citations
4
Methods Citations
2

24 Citations

Simplicity of twisted C*-algebras of higher-rank graphs and crossed products by quasifree actions

We characterise simplicity of twisted C*-algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the…

SIMPLICITY OF TWISTED C*-ALGEBRAS OF TOPOLOGICAL HIGHER-RANK GRAPHS

  • Becky Armstrong
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2020
In a recent series of papers, Kumjian, Pask and Sims [2–5] have investigated the effect of ‘twisting’ C∗-algebras associated to higher-rank graphs using a categorical 2-cocycle on the graph. This…

GRAPHS AND CROSSED PRODUCTS BY QUASIFREE ACTIONS

We characterise simplicity of twisted C � -algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the…

Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs

We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish…

Product-system models for twisted C⁎-algebras of topological higher-rank graphs

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

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…

K-theory and homotopies of twists on ample groupoids

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…

K-theory and homotopies of 2-cocycles on higher-rank graphs

This paper continues our investigation into the question of when a homotopy of 2-cocycles on a locally compact Hausdorff groupoid gives rise to an isomorphism of the K-theory groups of the twisted…

Topological spaces associated to higher-rank graphs

AF-embeddability of 2-graph algebras and quasidiagonality of k-graph algebras

References

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Homology for higher-rank graphs and twisted C*-algebras

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On the K-theory of higher rank graph C ∗ -algebras

Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C ∗ -algebra, C ∗ (Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of…

HOMOLOGY FOR HIGHER-RANK GRAPHS AND TWISTED

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Higher Rank Graph C-Algebras

Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that of…

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Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C *-algebra, C * (Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C…

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The K-Theory of Heegaard-Type Quantum 3-Spheres

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A Locally Trivial Quantum Hopf Fibration

Abstract The irreducible *-representations of the polynomial algebra $\mathcal{O}(S^{3}_{pq})$ of the quantum3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal…

Higher-Rank Graph C *-Algebras: An Inverse Semigroup and Groupoid Approach

AbstractWe provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the…