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Classification of injective factors
TLDR
Nann et al. as mentioned in this paper presented a survey of the main lines of the investigation in the classification of factors, culminating in the Connes-Takesakl structure theory of type III factors.Abstract:
The fundamental results of A. Connes which determine a complete set of isomorphism classes for most injectlve 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-Takesakl structure theory of type III factors. After a discussion of inJectlvity for finite factors, the main result of the paper, the uniqueness of the injectlve II 1 factor, is deduced, and the structure of II. and type III injectlve factors is then obtained as corollaries of the main result. 1980 AMS (MOS) SUBJECT CLASSIFICATION: PRIMARY 46L35, 46LI0; SECONDARY- 46L50, 46L05 KEY WORI)S AND PHRASES: jiVe yon Nann o.%gebra, fi facr, dcreread more
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