C*-algebras associated with Mauldin-Williams graphs

Marius Ionescu, Yasuo Watatani

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)545-560
Number of pages16
JournalCanadian Mathematical Bulletin
Volume51
Issue number4
DOIs
Publication statusPublished - Jan 1 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'C*-algebras associated with Mauldin-Williams graphs'. Together they form a unique fingerprint.

  • Cite this