A class of $C^*$-algebras generalizing both graph algebras and homeomorphism $C^*$-algebras IV, pure infiniteness

Details A class of $C^*$-algebras generalizing both graph algebras and homeomorphism $C^*$-algebras IV, pure infiniteness A class of $C^*$-algebras generalizing both graph algebras and homeomorphism $C^*$-algebras IV, pure infiniteness

2005-09-15

arxiv.org/abs/math/0509343v1

Mathematics

Operator Algebras

28 pages

Scientific paper

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.

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