The Dixmier-Douady invariant is the primary tool in the classification of continuous trace C*-algebras. These algebras have come to the fore in recent years because of their relationship to twisted K-theory and via twisted K-theory to branes, gerbes, and string theory.
This note sets forth the basic properties of the Dixmier-Douady invariant using only classical homotopy and bundle theory. Algebraic topology enters the scene at once since the algebras in question are algebras of sections of certain fibre bundles.
Algebra | Physical Sciences and Mathematics
C. Shochet, The Dixmier-Douady invariant for dummies, Notices of the American Mathematical Society 56.7 (2009), 809-816.