C*-Algebras Associated with Mauldin–Williams Graphs
Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 545-560
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A Mauldin–Williams graph $M$ is a generalization of an iterated function system by a directed graph. Its invariant set $K$ plays the role of the self-similar set. We associate a ${{C}^{*}}$ -algebra ${{O}_{M}}\left( K \right)$ with a Mauldin–Williams graph $M$ and the invariant set $K$ , laying emphasis on the singular points. We assume that the underlying graph $G$ has no sinks and no sources. If $M$ satisfies the open set condition in $K$ , and $G$ is irreducible and is not a cyclic permutation, then the associated ${{C}^{*}}$ -algebra ${{O}_{M}}\left( K \right)$ is simple and purely infinite. We calculate the $K$ -groups for some examples including the inflation rule of the Penrose tilings.
Ionescu, Marius; Watatani, Yasuo. C*-Algebras Associated with Mauldin–Williams Graphs. Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 545-560. doi: 10.4153/CMB-2008-054-0
@article{10_4153_CMB_2008_054_0,
author = {Ionescu, Marius and Watatani, Yasuo},
title = {C*-Algebras {Associated} with {Mauldin{\textendash}Williams} {Graphs}},
journal = {Canadian mathematical bulletin},
pages = {545--560},
year = {2008},
volume = {51},
number = {4},
doi = {10.4153/CMB-2008-054-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-054-0/}
}
TY - JOUR AU - Ionescu, Marius AU - Watatani, Yasuo TI - C*-Algebras Associated with Mauldin–Williams Graphs JO - Canadian mathematical bulletin PY - 2008 SP - 545 EP - 560 VL - 51 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-054-0/ DO - 10.4153/CMB-2008-054-0 ID - 10_4153_CMB_2008_054_0 ER -
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