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PERIODIC 2-GRAPHS ARISING FROM SUBSHIFTS

Published online by Cambridge University Press:  23 March 2010

DAVID PASK
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (email: [email protected])
IAIN RAEBURN*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (email: [email protected])
NATASHA A. WEAVER
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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Higher-rank graphs were introduced by Kumjian and Pask to provide models for higher-rank Cuntz–Krieger algebras. In a previous paper, we constructed 2-graphs whose path spaces are rank-two subshifts of finite type, and showed that this construction yields aperiodic 2-graphs whoseC*-algebras are simple and are not ordinary graph algebras. Here we show that the construction also gives a family of periodic 2-graphs which we call domino graphs. We investigate the combinatorial structure of domino graphs, finding interesting points of contact with the existing combinatorial literature, and prove a structure theorem for the C*-algebras of domino graphs.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

This research was supported by the Australian Research Council, and Natasha Weaver was supported by an Australian Postgraduate Award.

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