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Koichi Shimada (Kyoto University)
Tuesday 24 January 2017, 16:00-17:00
A classification of real-line group actions with faithful Connes--Takesaki modules on hyperfinite factors
- đ¤ Speaker: Koichi Shimada (Kyoto University)
- đ Date & Time: Tuesday 24 January 2017, 16:00 - 17:00
- đ Venue: Seminar Room 1, Newton Institute
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.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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