A characterization of semiprojectivity for subhomogeneous C*-algebras

TL;DR

This paper provides a detailed structural characterization of semiprojective subhomogeneous C*-algebras, including criteria based on primitive ideal spaces and direct limit structures, advancing understanding of their permanence properties.

Contribution

It introduces two new characterizations of semiprojectivity for subhomogeneous C*-algebras and explores their behavior under extensions, enriching the theory of these algebras.

Findings

Characterization via primitive ideal spaces

Description through direct limit structures over NCCW complexes

Complete analysis of semiprojectivity under extensions

Abstract

We study semiprojective, subhomogeneous C*-algebras and give a detailed description of their structure. In particular, we find two characterizations of semiprojectivity for subhomogeneous C*-algebras: one in terms of their primitive ideal spaces and one by means of special direct limit structures over one-dimensional NCCW complexes. These results are obtained by working out several new permanence results for semiprojectivity, including a complete description of its behavior with respect to extensions by homogeneous C*-algebras.