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

Authors:
Stephen Allen, David Pask and Aidan Sims

Journal:
Proc. Amer. Math. Soc. **134** (2006), 455-464

MSC (2000):
Primary 46L05

DOI:
https://doi.org/10.1090/S0002-9939-05-07994-3

Published electronically:
June 29, 2005

MathSciNet review:
2176014

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a -graph and an element of , we define the dual -graph, . We show that when is row-finite and has no sources, the -algebras and coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the -theory of when is finite and strongly connected and satisfies the aperiodicity condition.

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Additional Information

**Stephen Allen**

Affiliation:
Department of Mathematics, University of Newcastle, New South Wales 2308, Australia

Email:
stephen.allen@studentmail.newcastle.edu.au

**David Pask**

Affiliation:
Department of Mathematics, University of Newcastle, New South Wales 2308, Australia

Email:
david.pask@newcastle.edu.au

**Aidan Sims**

Affiliation:
Department of Mathematics, University of Newcastle, New South Wales 2308, Australia

Email:
aidan.sims@newcastle.edu.au

DOI:
https://doi.org/10.1090/S0002-9939-05-07994-3

Keywords:
Graphs as categories,
graph algebra,
$C^*$-algebra,
$K$-theory

Received by editor(s):
March 22, 2004

Received by editor(s) in revised form:
September 20, 2004

Published electronically:
June 29, 2005

Additional Notes:
This research was supported by the Australian Research Council.

Communicated by:
David R. Larson

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.