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

Abstract We investigate the structure of the fixed-point algebra of O n under the action of the cyclic permutation of the generating isometries. We prove that it is ⁎-isomorphic with O n , thus generalizing a result of Choi and Latremoliere on O 2 . As an application of the technique employed, we also describe the fixed-point algebra of O 2 n under the exchange automorphism.