On inductive limits of type I C*-algebras with one-dimensional spectrum

TL;DR

This paper classifies a specific class of separable C*-algebras, constructed as inductive limits of continuous-trace algebras with spectra resembling trees, using the Cuntz semigroup as the main invariant.

Contribution

It provides a classification of inductive limits of certain type I C*-algebras with one-dimensional spectra via the Cuntz semigroup, extending understanding of their structure.

Findings

Classification achieved using the Cuntz semigroup

Includes spectra homeomorphic to trees or trees with a point removed

Advances the understanding of inductive limits of type I C*-algebras

Abstract

The class of separable C*-algebras which can be written as inductive limits of continuous-trace C*-algebras with spectrum homeomorphic to a disjoint union of trees and trees with a point removed is classified by the Cuntz semigroup.