A Cantor spectrum diagonal in O_2

TL;DR

This paper demonstrates the existence of a specific diagonal subalgebra within the Cuntz algebra O_2, whose spectrum is topologically equivalent to the Cantor set, advancing understanding of the algebra's internal structure.

Contribution

It establishes the presence of a C*-diagonal in O_2 with a Cantor set spectrum, a novel structural insight into the algebra.

Findings

Existence of a C*-diagonal in O_2

Spectrum homeomorphic to the Cantor space

Advances understanding of O_2's structure

Abstract

We prove the existence of a C*-diagonal in the Cuntz algebra O_2 with spectrum homeomorphic to the Cantor space.