A class of \boldmath{$C^*$}-algebras generalizing both graph algebras and homeomorphism \boldmath{$C^*$}-algebras I, fundamental results
نویسندگان
چکیده
منابع مشابه
A Class of C∗-algebras Generalizing Both Graph Algebras and Homeomorphism C∗-algebras I, Fundamental Results
We introduce a new class of C∗-algebras, which is a generalization of both graph algebras and homeomorphism C∗-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem, and compute the K-groups of our algebras.
متن کاملA Class of C∗-algebras Generalizing Both Graph Algebras and Homeomorphism C∗-algebras Ii, Examples
We show that the method to construct C∗-algebras from topological graphs, introduced in our previous paper, generalizes many known constructions. We give many ways to make new topological graphs from old ones, and study the relation of C∗-algebras constructed from them. We also give a characterization of our C∗-algebras in terms of their representation theory.
متن کاملA Class of C∗-algebras Generalizing Both Graph Algebras and Homeomorphism C∗-algebras Iv, Pure Infiniteness
This is the final one in the series of papers where we introduce and study the C∗-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated C∗-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as C∗-algebras associated with topological graphs. 0. Introduc...
متن کاملA Class of C∗-algebras Generalizing Both Graph Algebras and Homeomorphism C∗-algebras Iii, Ideal Structures
We investigate the ideal structures of the C∗-algebras arising from topological graphs. We give the complete description of ideals of such C∗-algebras which are invariant under the so-called gauge action, and give the condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C∗algebras to be simple, prime or primitive. We completely deter...
متن کاملA Class of C * -algebras Generalizing Both Graph Algebras and Homeomorphism C
We introduce a new class of C∗-algebras, which is a generalization of both graph algebras and homeomorphism C∗-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the CuntzKrieger uniqueness theorem, and compute the K-groups of our algebras.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03636-0