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

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      Abstract

      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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      Journal
      15 September 2005
      math/0509343
      Custom metadata
      Primary 46L05; Secondary 46L55, 37B99
      28 pages
      math.OA

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