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

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 $\ast$-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.

arXiv commentAccepted for publication in J. Math. Anal. Appl

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Cited by in corpus (1)

• On the entropy and index of the winding endomorphisms of p-adic ring C${}^{\ast }$-algebras