On conjugacy of MASAs and the outer automorphism group of the Cuntz algebra

Abstract

We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of MASAa in $\mathcal{O}_n$. In particular, we exhibit an uncountable family of MASAs, conjugate to the standard MASA $\mathcal{D}_n$ via Bogolubov automorphisms, that are not inner conjugate to $\mathcal{D}_n$.