Timeline for Explicit cocycle for the central extension of the algebraic loop group G(C((t)))
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Mar 6, 2018 at 5:39 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
Replaced HTML with LaTeX
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| Jul 23, 2011 at 18:40 | history | edited | André Henriques | CC BY-SA 3.0 |
added a second reference
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| Jun 12, 2010 at 21:48 | vote | accept | André Henriques | ||
| May 17, 2010 at 9:11 | history | edited | André Henriques | CC BY-SA 2.5 |
deleted 32 characters in body; edited title
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| May 17, 2010 at 9:09 | comment | added | André Henriques | Sorry, my mistake! I forgot that C((t)) means the same thing as C[[t,t^-1]. | |
| May 16, 2010 at 23:13 | comment | added | Victor Protsak | Re new title: $C((t))$ is the field of formal Laurent series, which is the completion of the field of rational functions $C(t)$ at 0 or, alternatively, the field of fractions of the ring of formal power series $C[[t]].$ That is a right setting for a (completed) "algebraic loop group". But what do you mean by $C((t,t^{-1}))$? | |
| May 16, 2010 at 20:48 | history | edited | André Henriques | CC BY-SA 2.5 |
edited title
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| May 16, 2010 at 11:37 | comment | added | André Henriques | Actually, the above cocycle is continuous around the origin. So one gets the topology of \tilde{LG} in a neighborhood of its identity element. By translating it around, this can be used to define the topology everywhere. | |
| May 16, 2010 at 9:11 | comment | added | André Henriques | The above cocycle is discontinuous because the bounding discs D_gamma cannot be made to depend continuously on gamma. The [BCSS] paper does it a little bit differently, and also defines \tilde{LG} as a topological group. | |
| May 16, 2010 at 4:53 | answer | added | David Ben-Zvi | timeline score: 12 | |
| May 16, 2010 at 2:53 | comment | added | user6119 | You should look at the book by Pressley and Segal called Loop Groups. | |
| May 16, 2010 at 2:00 | history | edited | Allen Knutson | CC BY-SA 2.5 |
iint, iiint -> int
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| May 16, 2010 at 1:40 | comment | added | Victor Protsak | If I remember correctly, one difficulty in the (smooth or continuous) loop group case is that the central extension is topologically nontrivial. So one has to be careful by what is meant by the "cocycle for the central extension". | |
| May 16, 2010 at 1:23 | answer | added | Peter McNamara | timeline score: 8 | |
| May 16, 2010 at 0:23 | history | asked | André Henriques | CC BY-SA 2.5 |