TY - JOUR

T1 - C*-algebras associated with Mauldin-Williams graphs

AU - Ionescu, Marius

AU - Watatani, Yasuo

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2008/12

Y1 - 2008/12

N2 - 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 OM (K) 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 OM (K) is simple and purely infinite. We calculate the K-groups for some examples including the inflation rule of the Penrose tilings.

AB - 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 OM (K) 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 OM (K) is simple and purely infinite. We calculate the K-groups for some examples including the inflation rule of the Penrose tilings.

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U2 - 10.4153/CMB-2008-054-0

DO - 10.4153/CMB-2008-054-0

M3 - Article

AN - SCOPUS:57449098318

VL - 51

SP - 545

EP - 560

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

SN - 0008-4395

IS - 4

ER -