# $C^*$-algebras associated to coverings of $k$-graphs

@article{Kumjian2006CalgebrasAT, title={\$C^*\$-algebras associated to coverings of \$k\$-graphs}, author={Alex Kumjian and David Pask and Aidan Sims}, journal={Documenta Mathematica}, year={2006} }

A covering of k-graphs (in the sense of Pask-Quigg-Raeburn) induces an embedding of universal C*-algebras. We show how to build a (k+1)-graph whose universal algebra encodes this embedding. More generally we show how to realise a direct limit of k-graph algebras under embeddings induced from coverings as the universal algebra of a (k+1)-graph. Our main focus is on computing the K-theory of the (k+1)-graph algebra from that of the component k-graph algebras.
Examples of our construction include…

## 18 Citations

### Twisted k-Graph Algebras Associated to Bratteli Diagrams

- Mathematics
- 2014

Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite…

### Twisted k-Graph Algebras Associated to Bratteli Diagrams

- MathematicsIntegral Equations and Operator Theory
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Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite…

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- Mathematics
- 2007

In a number of recent papers, (k + l)-graphs have been constructed from k-graphs by inserting new edges in the last l dimensions. These constructions have been motivated by C � -algebraic…

### Simplicity of the C*-algebras of skew product k-graphs

- Mathematics
- 2013

We consider conditions on a $k$-graph $\Lambda$, a semigroup $S$ and a functor $\eta : \Lambda \to S$ which ensure that the $C^*$-algebra of the skew-product graph $\Lambda \times_\eta S$ is simple.…

### Real rank and topological dimension of higher rank graph algebras

- Mathematics
- 2015

We study dimension theory for the $C^*$-algebras of row-finite $k$-graphs with no sources. We establish that strong aperiodicity - the higher-rank analogue of condition (K) - for a $k$-graph is…

### On twisted higher-rank graph C*-algebras

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We define the categorical cohomology of a k-graphand show that the first three terms in this cohomology are isomorphic to the corresponding terms in the cohomology defined in our previous paper. This…

### Crossed products of k-graph C*-algebras by Zl

- Mathematics
- 2007

An action of Zl by automorphisms of a k-graph induces an action of Zl by automorphisms of the corresponding k-graph C*-algebra. We show how to construct a (k + l)-graph whose C*-algebra coincides…

### On k-morphs

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In a number of recent papers, (k + l)-graphs have been constructed from k-graphs by inserting new edges in the last l dimensions. These constructions have been motivated by C∗-algebraic…

### COVERINGS OF SKEW-PRODUCTS AND CROSSED PRODUCTS BY COACTIONS

- MathematicsJournal of the Australian Mathematical Society
- 2009

Abstract Consider a projective limit G of finite groups Gn. Fix a compatible family δn of coactions of the Gn on a C*-algebra A. From this data we obtain a coaction δ of G on A. We show that the…

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