Mathematics

The first classification result for infinite-dimensional C*-algebras is a natural generalization of the finite-dimensional case when considering M_n(C) as an inductive limit of itself over the identity *-homomorphism. It concerns the relationship between AF-algebras and Bratteli diagrams, or equivalently, K_0-groups. Adding more K-theoretical data a larger class of inductive limit C*-algebras can be classified and other inductive limits have been proven to be not in the Elliott conjecture class. 

In the category of C*-algebras, a central role is played by the strongly self-absorbing ones and in the finite case the only known examples of such are inductive limit C*-algebras.