Timeline for subfactor of finite rank but infinite index: is this possible?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Mar 8, 2016 at 17:38 | answer | added | Marcel Bischoff | timeline score: 1 | |
| Nov 29, 2010 at 7:43 | history | edited | André Henriques | CC BY-SA 2.5 |
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| Oct 29, 2010 at 15:56 | history | edited | André Henriques | CC BY-SA 2.5 |
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| Oct 11, 2010 at 8:57 | answer | added | Makoto Yamashita | timeline score: 5 | |
| Oct 9, 2010 at 0:24 | comment | added | Jon Bannon | Sorry, Andre. I assumed your notion of depth was the standard one, and posted what knew quickly in order to help. I should have more carefully considered your definition! Answer deleted. | |
| Oct 7, 2010 at 19:49 | history | edited | André Henriques | CC BY-SA 2.5 |
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| Oct 7, 2010 at 16:12 | comment | added | Noah Snyder | I think "finite rank" is the best term for what you're looking for. The "depth" of a subfactor tells you how high a power of the generating object you need to look in to find everything, while the "rank" is the number of simple objects. Even for finite index finite depth subfactors the depth and the rank are typically different, but in the finite index case you know that each depth only has finitely many new objects. | |
| Oct 7, 2010 at 15:36 | history | edited | André Henriques | CC BY-SA 2.5 |
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| Oct 7, 2010 at 15:35 | comment | added | André Henriques | @pasquale: Sorry. My use of the term "finite depth" was misguided (what term should I use then?). But you're perfectly right: I care about something like a fusion category where objects are allowed to have infinite dimension. | |
| Oct 7, 2010 at 9:56 | comment | added | pasquale zito | I think the usual definition of finite depth, when dealing with infinite index, is to say that all isomorphism classes are generated by a finite iteration of the basic construction. With this definition, the outer action of a compact group on a factor would provide a positive answer to Question 1 (a depth 2 irr. infinite index subfactor). But you seem to be interested in something different, something like a fusion category where objects are allowed to have infinite dimension, is that right? | |
| Oct 6, 2010 at 20:42 | history | asked | André Henriques | CC BY-SA 2.5 |