On Conjugacy of MASAs and the Outer Automorphism Group of the Cuntz Algebra

TL;DR

This paper explores the structure of the outer automorphism group of the Cuntz algebra and demonstrates the existence of uncountably many MASAs conjugate to the standard MASA via automorphisms but not inner conjugate.

Contribution

It provides the first example of uncountably many MASAs conjugate via automorphisms but not inner conjugate to the standard MASA in the Cuntz algebra.

Findings

Existence of uncountably many MASAs not inner conjugate to D_n

Construction of MASAs conjugate via Bogolubov automorphisms

Insights into the automorphism group structure of 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 O_n. In particular, we exhibit an uncountable family of MASAs, conjugate to the standard MASA D_n via Bogolubov automorphisms, that are not inner conjugate to D_n.