On twisted higher-rank graph $C^*$-algebras
نویسندگان
چکیده
منابع مشابه
Higher Rank Graph C∗-algebras
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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These are lecture notes of a course given by Alex Kumjian at the RMMC Summer School at the University of Wyoming, Laramie, June 1-5, 2015. Warning: little proofreading has been done.
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Let F+θ be a k-graph on a single vertex. We show that every irreducible atomic ∗-representation is the minimal ∗-dilation of a group construction representation. It follows that every atomic representation decomposes as a direct sum or integral of such representations. We characterize periodicity of F+θ and identify a symmetry subgroup Hθ of Z. If this has rank s, then C(Fθ ) ∼= C(T) ⊗ A for so...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2015
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2015-06209-6