Decomposition rank of approximately subhomogeneous C*-algebras

TL;DR

This paper proves that Jiang-Su stable approximately subhomogeneous C*-algebras have finite decomposition rank, advancing understanding of their structural properties and implications for related crossed products.

Contribution

It establishes the finite decomposition rank for a broad class of C*-algebras previously not known to have this property, using local approximation techniques.

Findings

Jiang-Su stable approximately subhomogeneous C*-algebras have finite decomposition rank

Subhomogeneous C*-algebras can be locally approximated by non-commutative cell complexes

Jiang-Su stable minimal Z-crossed products also have finite decomposition rank

Abstract

It is shown that every Jiang-Su stable approximately subhomogeneous C*-algebra has finite decomposition rank. Previously, it was not even known that such algebras have finite nuclear dimension. A key step in the proof is that subhomogeneous C*-algebra are locally approximated by a certain class of more tractable subhomogeneous algebras, namely, a non-commutative generalization of the class of cell complexes. The result is applied to show that Jiang-Su stable minimal Z-crossed products have finite decomposition rank.