Dixmier-Douady for Dummies

TL;DR

This paper explains the Dixmier-Douady invariant, a key concept in classifying continuous trace C*-algebras, using classical algebraic topology to clarify its properties.

Contribution

It provides an accessible exposition of the Dixmier-Douady invariant through the lens of algebraic topology, enhancing understanding of its role in C*-algebra classification.

Findings

Clarifies properties of the Dixmier-Douady invariant

Connects algebraic topology with C*-algebra classification

Simplifies understanding of continuous trace C*-algebras

Abstract

The Dixmier-Douady invariant is the primary tool in the classification of continuous trace $C^*$-algebras. This expository note explores its properties from the perspective of classical algebraic topology.