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K-theory for Cuntz–Krieger algebras is very important not only for classification theory of \(C^*\) -algebras but also for classification theory of topological Markov shifts. In this chapter, we will first prove that the Cuntz–Krieger algebras \(\mathcal {O}_A\) are purely infinite for all irreducible non-permutation matrices A with entries in \(\{0,1\}\) . We will second compute the K-theory groups for the Cuntz–Krieger algebras.

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K-Theory for Cuntz–Krieger Algebras

  • 章节

  • 发表日期：

    2025年

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  • Kengo Matsumoto

摘要

K-theory for Cuntz–Krieger algebras is very important not only for classification theory of \(C^*\) -algebras but also for classification theory of topological Markov shifts. In this chapter, we will first prove that the Cuntz–Krieger algebras \(\mathcal {O}_A\) are purely infinite for all irreducible non-permutation matrices A with entries in \(\{0,1\}\) . We will second compute the K-theory groups for the Cuntz–Krieger algebras.