Classification of injective factors: The wok of Alain Connes
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 investigat...
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171283000010 |
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| _version_ | 1832552035591913472 |
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| author | Steve Wright |
| author_facet | Steve Wright |
| author_sort | Steve Wright |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-aa499ba821184a9a90d6b16d033a48f2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-aa499ba821184a9a90d6b16d033a48f22025-02-03T05:59:52ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016113910.1155/S0161171283000010Classification of injective factors: The wok of Alain ConnesSteve Wright0Department of Mathematical Sciences, Oakland University, Rochester 48063, Michigan, USAThe 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.http://dx.doi.org/10.1155/S0161171283000010injective von Neumann algebrafinite factordiscrete and continuous crossed productsinfinite tensor productsemidiscrete von Neumann algebra. |
| spellingShingle | Steve Wright Classification of injective factors: The wok of Alain Connes International Journal of Mathematics and Mathematical Sciences injective von Neumann algebra finite factor discrete and continuous crossed products infinite tensor product semidiscrete von Neumann algebra. |
| title | Classification of injective factors: The wok of Alain Connes |
| title_full | Classification of injective factors: The wok of Alain Connes |
| title_fullStr | Classification of injective factors: The wok of Alain Connes |
| title_full_unstemmed | Classification of injective factors: The wok of Alain Connes |
| title_short | Classification of injective factors: The wok of Alain Connes |
| title_sort | classification of injective factors the wok of alain connes |
| topic | injective von Neumann algebra finite factor discrete and continuous crossed products infinite tensor product semidiscrete von Neumann algebra. |
| url | http://dx.doi.org/10.1155/S0161171283000010 |
| work_keys_str_mv | AT stevewright classificationofinjectivefactorsthewokofalainconnes |