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PERIODIC 2-GRAPHS ARISING FROM SUBSHIFTS

Part of: Selfadjoint operator algebras Locally compact groups and their algebras

Published online by Cambridge University Press:  23 March 2010

DAVID PASK ,
IAIN RAEBURN  and
NATASHA A. WEAVER
DAVID PASK
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (email: dpask@uow.edu.au)
IAIN RAEBURN*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (email: raeburn@uow.edu.au)
NATASHA A. WEAVER
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia (email: Tash.Weaver@gmail.com)
*
✉For correspondence; e-mail: raeburn@uow.edu.au
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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.

Keywords

2-graphsubshiftgraph algebracrossed productinduced C*-algebra

MSC classification

Secondary: 46L55: Noncommutative dynamical systems 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 1 , August 2010 , pp. 120 - 138
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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