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

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.