Structure and classification of C.-algebras

• Autores: Mikael Rordam
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé , Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 1581-1598
• Idioma: inglés
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• Resumen

  • 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 matrices 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.