# COVERINGS OF SKEW-PRODUCTS AND CROSSED PRODUCTS BY COACTIONS

@article{Pask2007COVERINGSOS, title={COVERINGS OF SKEW-PRODUCTS AND CROSSED PRODUCTS BY COACTIONS}, author={David Pask and John Quigg and Aidan Sims}, journal={Journal of the Australian Mathematical Society}, year={2007}, volume={86}, pages={379 - 398} }

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 coaction crossed product of A by δ is isomorphic to a direct limit of the coaction crossed products of A by the δn. If A=C*(Λ) for some k-graph Λ, and if the coactions δn correspond to skew-products of Λ, then we can say more. We prove that the coaction crossed product of C*(Λ) by δ may be realized as a…

## 4 Citations

### On k-morphs

- 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…

### GENERALISED MORPHISMS OF k-GRAPHS: k-MORPHS

- 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…

### Topological realizations and fundamental groups of higher-rank graphs

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2015

Abstract We investigate topological realizations of higher-rank graphs. We show that the fundamental group of a higher-rank graph coincides with the fundamental group of its topological realization.…

### LECTURE NOTES ON HIGHER-RANK GRAPHS AND THEIR C -ALGEBRAS

- Mathematics
- 2010

These are notes for a short lecture course on k-graph C -algebras to be delivered at the Summer School on C -algebras and their interplay with dynamics at the Sophus Lie Conference Centre in…

## References

SHOWING 1-10 OF 25 REFERENCES

### Mansfield’s imprimitivity theorem for full crossed products

- Mathematics
- 2004

For any maximal coaction (A, G, S) and any closed normal subgroup N of G, there exists an imprimitivity bimodule Y G G/N (A) between the full crossed product A × δ G × δ| N and A × δ| G/N, together…

### On higher rank graph C ∗ -algebras

- Mathematics
- 2000

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…

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

- Mathematics, Computer ScienceDocumenta Mathematica
- 2008

This work shows how to realise a direct limit of k-graph algebras under embeddings induced from coverings as the universal algebra of a (k+1-graph) whose universal algebra encodes this embedding.

### Graphs, Groupoids, and Cuntz–Krieger Algebras

- Mathematics
- 1997

We associate to each locally finite directed graphGtwo locally compact groupoidsGandG(★). The unit space ofGis the space of one–sided infinite paths inG, andG(★) is the reduction ofGto the space of…

### CUNTZ-KRIEGER ALGEBRAS OF DIRECTED GRAPHS

- Mathematics
- 1998

We associate to each row-nite directed graph E a universal Cuntz-Krieger C-algebra C(E), and study how the distribution of loops in E aects the structure of C(E) .W e prove that C(E) is AF if and…

### Simplicity of C*‐algebras associated to higher‐rank graphs

- Mathematics
- 2007

We prove that if Λ is a row‐finite k‐graph with no sources, then the associated C*‐algebra is simple if and only if Λ is cofinal and satisfies Kumjian and Pask's aperiodicity condition, known as…

### Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras

- Mathematics
- 1999

To an $r$-dimensional subshift of finite type satisfying certain special properties we associate a $C^*$-algebra $\cA$. This algebra is a higher rank version of a Cuntz-Krieger algebra. In…

### Groupoid models for the C*-algebras of topological higher-rank graphs

- Mathematics
- 2006

We provide groupoid models for Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs. Extending the groupoid models used in the theory of graph algebras and topological dynamical…

### Duality theory for covariant systems

- Mathematics
- 1979

If (A, p, G) is a covariant system over a locally compact group G, i.e. p is a homomorphism from G into the group of *-automorphisms of an operator algebra A, there is a new operator algebra W called…