Recursive subhomogeneity of orbit-breaking subalgebras of $\mathrm{C}^*$-algebras associated to minimal homeomorphisms twisted by line bundles

TL;DR

This paper develops a recursive subhomogeneous decomposition for Cuntz--Pimsner algebras derived from orbit-breaking in minimal dynamical systems, extending previous results for crossed product algebras.

Contribution

It generalizes recursive subhomogeneous decompositions to Cuntz--Pimsner algebras associated with orbit-breaking, broadening the understanding of their structure.

Findings

Established recursive subhomogeneous decomposition for these algebras

Extended known results from crossed products to Cuntz--Pimsner algebras

Provided a new structural framework for orbit-breaking subalgebras

Abstract

In this paper, we construct a recursive subhomogeneous decomposition for the Cuntz--Pimsner algebras obtained from breaking the orbit of a minimal Hilbert $C(X)$-bimodule at a subset $Y \subset X$ with non-empty interior. This generalizes the known recursive subhomogeneous decomposition for orbit-breaking subalgebras of crossed products by minimal homeomorphisms.