Mathematical analysis demonstrates homotopy groups serve as complete invariants for Cuntz-Krieger algebras, highlighting characterization via extension groups.
In this paper, we first present the homotopy groups of the automorphism groups of Cuntz--Krieger algebras in terms of the underlying matrices of the Cuntz--Krieger algebras. We also show that the homotopy groups are complete invariants of the isomorphism class of the Cuntz--Krieger algebras. As a result, the isomorphism type of Cuntz--Krieger algebras are completely characterized by the group structure of the weak and strong extension groups.
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Matsumoto et al. (2024) studied this question.
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