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arXiv · 2107.02154

On the cyclic automorphism of the Cuntz algebra and its fixed-point algebra

Valeriano Aiello·Stefano Rossi
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Abstract

We investigate the structure of the fixed-point algebra of $\mathcal{O}_n$ under the action of the cyclic permutation of the generating isometries. We prove that it is $*$-isomorphic with $\mathcal{O}_n$, thus generalizing a result of Choi and Latrémolière on $\mathcal{O}_2$. As an application of the technique employed, we also describe the fixed-point algebra of $\mathcal{O}_{2n}$ under the exchange automorphism.

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Valeriano Aiello, Stefano Rossi. 2021-07-05. On the cyclic automorphism of the Cuntz algebra and its fixed-point algebra. https://doi.org/10.1016/j.jmaa.2021.125476

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