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arXiv · 1903.04809

The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra

Masaki Izumi·Taro Sogabe
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Abstract

We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra $O_{n+1}$ for finite n in terms of K-theory. We show that there is an example of a space for which the homotopy set is a non-commutative group, and hence the classifying space of the automorphism group of the Cuntz algebra for finite n is not an H-space. We also make an improvement of Dadarlat's classification of continuous fields of the Cuntz algebras in terms of vector bundles.

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Masaki Izumi, Taro Sogabe. 2019-03-12. The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra. https://arxiv.org/abs/1903.04809

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