Structure and classification of C*-algebras [chapter]

Mikael Rørdam
Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006  
We give an overview of the development over the last 15 years of the theory of simple C * -algebras, in particular in regards to their classification and structure. We discuss dimension theory for (simple) C * -algebras, in particular the so-called stable and real ranks, and we explain how properties of C * -algebras of low dimension (stable rank one and real rank zero) was used by the author and P. Friis to give a new and simple proof of a theorem of H. Lin that almost commuting self-adjoint
more » ... trices are close to exactly commuting self-adjoint matrices. Elliott's classification program is explained and is contrasted with recent examples of C * -algebras of "high dimension", including an example of a simple C * -algebra with a finite and an infinite projection. (2000) . Primary 46L35; Secondary 46L80. Mathematics Subject Classification
doi:10.4171/022-2/75 fatcat:zwn36narnja4thiiy4fccnarqe