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A family of 2-graphs arising from two-dimensional subshifts

Published online by Cambridge University Press:  12 March 2009

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

Higher-rank graphs (or k-graphs) were introduced by Kumjian and Pask to provide combinatorial models for the higher-rank Cuntz–Krieger C*-algebras of Robertson and Steger. Here we consider a family of finite 2-graphs whose path spaces are dynamical systems of algebraic origin, as studied by Schmidt and others. We analyse the C*-algebras of these 2-graphs, find criteria under which they are simple and purely infinite, and compute their K-theory. We find examples whose C*-algebras satisfy the hypotheses of the classification theorem of Kirchberg and Phillips, but are not isomorphic to the C*-algebras of ordinary directed graphs.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 5 , October 2009 , pp. 1613 - 1639
Copyright
Copyright © Cambridge University Press 2009

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