Higher-Rank Graph C *-Algebras: An Inverse Semigroup and Groupoid Approach
نویسندگان
چکیده
منابع مشابه
Higher-rank Graph C∗-algebras: an Inverse Semigroup and Groupoid Approach
We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.
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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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Abstract. Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C-algebra, C(Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C(Λ). The Kgroups of C(Λ) for k > 2 can be calculated under certain circumstances and we consider the case k = 3. We prove that for arbitrary k, the torsion-free rank of K0(C∗(Λ)) and K1(C∗(Λ)) ...
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ژورنال
عنوان ژورنال: Semigroup Forum
سال: 2005
ISSN: 0037-1912,1432-2137
DOI: 10.1007/s00233-005-0512-2