Pure infiniteness, stability and C*-algebras of graphs and dynamical systems

Details Pure infiniteness, stability and C*-algebras of graphs and dynamical systems Pure infiniteness, stability and C*-algebras of graphs and dynamical systems

1999-06-29

arxiv.org/abs/math/9906201v1

Mathematics

Operator Algebras

31 pages

Scientific paper

Pure infiniteness (in sense of E.Kirchberg and M.R{\o}rdam) is considered for C*-algebras arising from singly generated dynamical systems. In particular, Cuntz-Krieger algebras and their generalizations, i.e., graph-algebras and O_A 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.

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