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

Title: A family of 2-graphs arising from two-dimensional subshifts
Creator: Pask, David; Raeburn, Iain; Weaver, Natasha A.
Relation: ARC
Relation: Ergodic Theory and Dynamical Systems Vol. 29, Issue 5, p. 1613-1639
Publisher Link: http://dx.doi.org/10.1017/S0143385708000795
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2009
Description: 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.
Subject: higher-rank graph; Cuntz-Krieger algebras; C*-algebras
Identifier: http://hdl.handle.net/1959.13/1057820
Identifier: uon:16275
Identifier: ISSN:0143-3857
Language: eng
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