# A dual graph construction for higher-rank graphs, and K-theory for finite 2-graphs

@inproceedings{Allen2004ADG, title={A dual graph construction for higher-rank graphs, and K-theory for finite 2-graphs}, author={Stephen Allen and David Pask and Aidan Sims}, year={2004} }

Given a k-graph A and an element p of N k , we define the dual k-graph, pA. We show that when A is row-finite and has no sources, the C*-algebras C*(A) and C*(pA) coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the K-theory of C*(A) when A is finite and strongly connected and satisfies the aperiodicity condition.

## 15 Citations

### Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs

- Mathematics
- 2007

In a previous work, the authors showed that the C*-algebra C*(Λ) of a row-finite higher-rank graph Λ with no sources is simple if and only if Λ is both cofinal and aperiodic. In this paper, we…

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

- Mathematics
- 2004

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…

### Gauge Invariant Uniqueness Theorem for Corners of k-graphs

- Mathematics
- 2005

. For a ﬁnitely aligned k -graph Λ with X a set of vertices in Λ we deﬁne a universal C ∗ -algebra called C ∗ (Λ ,X ) generated by partial isometries. We show that C ∗ (Λ ,X ) is isomorphic to the…

### Algebras of Higher Rank Graphs

- Mathematics

We begin the study of a new class of operator algebras that arise from higher rank graphs. Every higher rank graph generates a Fock space Hilbert space and creation operators which are partial…

### The $H^\infty$ algebras of higher rank graphs

- Mathematics
- 2004

We begin the study of a new class of operator algebras that arise from higher rank graphs. Every higher rank graph generates a Fock space Hilbert space and creation operators which are partial…

### THE ANALYTIC ALGEBRAS OF HIGHER RANK GRAPHS

- MathematicsMathematical Proceedings of the Royal Irish Academy
- 2006

We begin the study of a new class of operator algebras that arise from higher rank graphs. Every higher rank graph generates a Fock space Hubert space and creation operators that are partial…

### 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…

### 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…

### THE K-THEORY OF SOME HIGHER RANK EXEL–LACA ALGEBRAS

- MathematicsJournal of the Australian Mathematical Society
- 2008

Abstract Let $\mathcal {O}$ be a higher rank Exel–Laca algebra generated by an alphabet $\mathcal {A}$. If $\mathcal {A}$ contains d commuting isometries corresponding to rank d and the transition…

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