Poly-$\mathbb{Z}$ group actions on Kirchberg algebras II

TL;DR

This paper advances the classification of poly-$\mathbb{Z}$ group actions on Kirchberg algebras by reducing the problem to classifying continuous fields and determining cocycle conjugacy classes of outer $\mathbb{Z}^n$-actions.

Contribution

It provides a complete reduction of the classification problem to continuous fields and counts cocycle conjugacy classes for outer $\mathbb{Z}^n$-actions on Cuntz algebras.

Findings

Reduced classification to continuous fields over classifying spaces

Determined the number of cocycle conjugacy classes of outer $\mathbb{Z}^n$-actions

Extended previous work on poly-$\mathbb{Z}$ group actions

Abstract

This is the second part of our serial work on the classification of poly-$\mathbb{Z}$ group actions on Kirchberg algebras. Based on technical results obtained in our previous work, we completely reduce the problem to the classification of continuous fields of Kirchberg algebras over the classifying spaces. As an application, we determine the number of cocycle conjugacy classes of outer $\mathbb{Z}^n$-actions on the Cuntz algebras.