Cuntz--Pimsner algebras of partial automorphisms twisted by vector bundles II: Nuclear dimension

TL;DR

This paper proves that Cuntz--Pimsner algebras from partial automorphisms twisted by vector bundles are classifiable under certain conditions, and explores their trace space, extending prior results in the field.

Contribution

It establishes classification results for these algebras when the action is minimal and the base space is compact, infinite, with finite covering dimension, and analyzes their tracial states.

Findings

Algebras are classifiable under specified conditions.

Tracial states correspond to conformal measures.

Generalizes previous results on orbit-breaking subalgebras.

Abstract

We show that Cuntz--Pimsner algebras associated to partial automorphisms twisted by vector bundles are classifiable in the sense of the Elliott program whenever the action is minimal and the base space is compact, infinite and has finite covering dimension. We also investigate the tracial state space of our algebras, and show that traces are in bijection to certain conformal measures. This generalizes results about partial crossed products by Geffen and complements results about the $C^*$-algebras associated to homeomorphisms twisted by vector bundles of Adamo, Archey, Forough, Georgescu, Jeong, Strung and Viola. We use our findings to generalize various existing statements about orbit-breaking subalgebras.