On Normalizers of $C^*$-Subalgebras in the Cuntz Algebra ${\mathcal O}_n$. II

TL;DR

This paper characterizes the normalizer groups of certain subalgebras within the Cuntz algebra ${ m O}_n$, specifically those formed as finite sums of corners of the UHF-subalgebra ${ m F}_n$, advancing understanding of their symmetries.

Contribution

It provides a complete description of the normalizer groups for subalgebras that are finite sums of corners of ${ m F}_n$ within ${ m O}_n$, a specific class not fully understood before.

Findings

Normalizers are explicitly characterized for the subalgebras considered.

The structure of the normalizer groups depends on the configuration of the corners.

Results extend the understanding of symmetries in Cuntz algebras.

Abstract

We investigate subalgebras $A$ of the Cuntz algebra ${\mathcal O}_n$ that arise as finite direct sums of corners of the UHF-subalgebra ${\mathcal F}_n$. For such an $A$, we completely determine its normalizer group inside ${\mathcal O}_n$.