A family of 2-graphs arising from two-dimensional subshifts
| dc.creator | Pask, David | |
| dc.creator | Raeburn, Iain | |
| dc.creator | Weaver, Natasha A. | |
| dc.date | 2008-04-22 | |
| dc.date.accessioned | 2026-07-07T09:33:58Z | |
| dc.date.available | 2026-07-07T09:33:58Z | |
| dc.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. | |
| dc.description | 28 pages, 3 figures, 1 table | |
| dc.identifier | https://arxiv.org/abs/0804.3447 | |
| dc.identifier | http://arxiv.org/abs/0804.3447 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159322 | |
| dc.subject | Operator Algebras | |
| dc.subject | Dynamical Systems | |
| dc.subject | 46L05; 37B50 | |
| dc.title | A family of 2-graphs arising from two-dimensional subshifts | |
| dc.type | text |