The classification ofseparable simple C*-algebras which are inductive limits of continuous-trace C*-algebraswith spectrum homeomorphic to the closed interval [0,1]

TL;DR

This paper classifies a specific class of separable simple nuclear C*-algebras that are inductive limits of continuous-trace C*-algebras with spectrum [0,1], extending understanding beyond real rank zero cases.

Contribution

It provides a classification of certain separable simple nuclear C*-algebras as inductive limits of continuous-trace algebras with spectrum [0,1], including the calculation of their invariant range.

Findings

Classification of these C*-algebras achieved

Range of the invariant explicitly calculated

Extends classification beyond real rank zero

Abstract

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of separable simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have spectrum homeomorphic to the closed interval [0,1], or to a disjoint union of copies of this space. Also, the range of the invariant is calculated.