A classification of real-line group actions with faithful Connes--Takesaki modules on hyperfinite factors
Duration: 1 hour 2 mins
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About this item
| Description: |
Shimada, K (Kyoto University)
Tuesday 24th January 2017 - 16:00 to 17:00 |
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| Created: | 2017-02-08 15:33 |
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| Collection: | Operator algebras: subfactors and their applications |
| Publisher: | Isaac Newton Institute |
| Copyright: | Shimada, K |
| Language: | eng (English) |
| Abstract: | We classify certain real-line-group actions on (type III) hyperfinite factoers, up to cocycle conjugacy. More precisely, we show that an invariant called the Connes--Takesaki module completely distinguishs actions which are not approximately inner at any non-trivial point. Our classification result is related to the uniqueness of the hyperfinite type III_1 factor, shown by Haagerup, which is equivalent to the uniquness of real-line-group actions with a certain condition on the hyperfinite type II_{\infty} factor. We classify actions on hyperfinite type III factors with an analogous condition. The proof is based on Masuda--Tomatsu's recent work on real-line-group actions and the uniqueness of the hyperfinite type III_1 factor.
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