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arXiv · 2404.06115

On the homotopy groups of the automorphism groups of Cuntz-Krieger algebras

Kengo Matsumoto·Taro Sogabe
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Abstract

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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Kengo Matsumoto, Taro Sogabe. 2024-04-09. On the homotopy groups of the automorphism groups of Cuntz-Krieger algebras. https://arxiv.org/abs/2404.06115

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