Nuclear dimension of extensions of $\mathcal{O}_\infty$-stable algebras

TL;DR

This paper improves the upper bounds on the nuclear dimension of extensions of algebra-stable algebras, showing that certain full extensions have nuclear dimension one, advancing understanding in operator algebra classification.

Contribution

It provides a new upper bound for the nuclear dimension of extensions of algebra-stable algebras, specifically proving that certain full extensions have nuclear dimension one.

Findings

Nuclear dimension of extensions of algebra-stable algebras is bounded above by a smaller number.

Full extensions of algebra-stable algebras by stable AF algebras have nuclear dimension one.

The result refines previous bounds and contributes to classification theory.

Abstract

We obtain an improved upper bound for the nuclear dimension of extensions of $\mathcal{O}_\infty$-stable $\rm{C}^*$-algebras. In particular, we prove that the nuclear dimension of a full extension of an $\mathcal{O}_\infty$-stable $\rm{C}^*$-algebra by a stable AF algebra is one.