HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS
نویسندگان
چکیده
منابع مشابه
Lecture Notes on Higher-rank Graphs and Their C∗-algebras
These are notes for a short lecture course on k-graph C∗-algebras to be delivered at the Summer School on C∗-algebras and their interplay with dynamics at the Sophus Lie Conference Centre in Nordfjordeid, Norway in June 2010. They are not even remotely comprehensive of the work that many authors have done on k-graphs, nor are all details even of the material covered included. In addition, there...
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We prove that if Λ is a row-finite k-graph with no sources, then the associated C∗-algebra is simple if and only if Λ is cofinal and satisfies Kumjian and Pask’s Condition (A). We prove that Condition (A) is equivalent to a suitably modified version of Robertson and Steger’s original nonperiodicity condition (H3) which in particular involves only finite paths. We also characterise both cofinali...
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Building on recent work of Robertson and Steger, we associate a C∗–algebra to a combinatorial object which may be thought of as a higher rank graph. This C∗–algebra is shown to be isomorphic to that of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C∗–algebra to be: simple, purely infinite and AF. Results concer...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2003
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091501000645