Pure infiniteness, stability and C-algebras of graphs and dynamical systems
نویسنده
چکیده
Pure infiniteness (in sense of [11]) is considered for C∗-algebras arising from singly generated dynamical systems. In particular, Cuntz-Krieger algebras and their generalizations, i.e., graph-algebras and OA of an infinite matrix A, admit characterizations of pure infiniteness. As a consequence, these generalized Cuntz-Krieger algebras are traceless if and only if they are purely infinite. Also, a characterization of AF-algebras among these C∗-algebras is given. In the case of graph-algebras of locally finite graphs, characterizations of stability are obtained.
منابع مشابه
Cuntz-like Algebras
The usual crossed product construction which associates to the homeomorphism T of the locally compact space X the C∗-algebra C∗(X, T ) is extended to the case of a partial local homeomorphism T . For example, the Cuntz-Krieger algebras are the C∗-algebras of the one-sided Markov shifts. The generalizations of the Cuntz-Krieger algebras (graph algebras, algebras OA where A is an infinite matrix)...
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