International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 1, Pages 1-39

Classification of injective factors: The wok of Alain Connes

Steve Wright

Department of Mathematical Sciences, Oakland University, Rochester 48063, Michigan, USA

Received 7 May 1981

Copyright © 1983 Steve Wright. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The fundamental results of A. Connes which determine a complete set of isomorphism classes for most injective factors are discussed in detail. After some introductory remarks which lay the foundation for the subsequent discussion, an historical survey of some of the principal lines of the investigation in the classification of factors is presented, culminating in the Connes-Takesaki structure theory of type III factors. After a discussion of injectivity for finite factors, the main result of the paper, the uniqueness of the injective II1 factor, is deduced, and the structure of II and type III injective factors is then obtained as corollaries of the main result.