Elliott classification program

Summary

The Elliott classification program aims to classify separable, simple, nuclear C*-algebras up to isomorphism. The invariant, called the Elliott invariant, is built from K-theory and traces. It grew out of Elliott's classification of AF algebras by their ordered $K_0$-groups. Counterexamples of Rørdam and Toms show that the invariant does not classify all simple separable nuclear C*-algebras, so a regularity hypothesis is needed. The classification is now a theorem, due to many authors, for unital, simple, separable C*-algebras of finite nuclear dimension in the UCT class.