Timeline for "Non-group" ${\rm II}_1$ factors
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| Jul 8, 2020 at 19:36 | comment | added | Jon Bannon | For your second question, the answer is no. See Proposition 10.1.3 and Proposition 10.2.2 here: idpoisson.fr/anantharaman/publications/IIun.pdf (Here I have assumed that your G is i.c.c. and discrete. The situation is more complicated in general.) As you can see, your questions are pretty good ones, even though the answers are known. Keep on trucking! | |
| Jul 8, 2020 at 19:31 | comment | added | Jon Bannon | For your first question: Yes. See V.F.R. Jones "A II_1 factor anti-isomorphic to itself but without involutory antiautomorphisms", Math. Scand. 46 (1990) 103-117. In fact, this question is probably a duplicate (mathoverflow.net/questions/345844/…) | |
| Jul 8, 2020 at 18:45 | comment | added | Chilperic | Thanks. Naturally, if the "antiisomorphic to itself" is only a necessary property of group factors, it leads to the question, are there antiisomorphic to itself II_1 factors that are not group factors? And since we are on a roll, are there non-amenable groups for which L(G) is hyperfinite? Or should I pose these as separate questions on MO here? | |
| Jul 8, 2020 at 17:38 | history | edited | YCor |
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| Jul 8, 2020 at 17:04 | comment | added | Jon Bannon | Yes. This was established by Connes in 1975. Every L(G) is antiisomorphic to itself, but there exist II_1 factors without this property. See Connes, Alain "Sur la classification des facteurs de type II", C.R. Acad. Sci. Paris Ser A-B 281 (1975), 13-15. | |
| Jul 8, 2020 at 16:04 | history | asked | Chilperic | CC BY-SA 4.0 |