Timeline for 2-cocycle on LSU(2)
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| S Mar 9, 2012 at 12:34 | vote | accept | Damien S. | ||
| S Mar 9, 2012 at 12:34 | vote | accept | Damien S. | ||
| S Mar 9, 2012 at 12:34 | |||||
| Mar 9, 2012 at 12:34 | vote | accept | Damien S. | ||
| S Mar 9, 2012 at 12:34 | |||||
| Mar 8, 2012 at 2:58 | answer | added | Konrad Waldorf | timeline score: 4 | |
| Mar 7, 2012 at 16:38 | comment | added | André Henriques | The map $\omega:LG\times LG\to \mathbb S^1$ cannot be chosen continuous. There are two ways of dealing with that situation: either you take it to be (piecewise smooth) discontinuous, or you take it to be smooth but multivalued. The second definition of cocycle is somewhat more technical, but I think more powerful. | |
| Mar 7, 2012 at 16:26 | comment | added | Damien S. | I mean a (smooth) map $\omega: LG\times LG \to \mathbb{C}^\times$ that satisfies the 2-co-cycle property. The Lie algebra $L\mathfrak{g}$ has an easy non-trivial 2-cocycle given by \begin{equation} \kappa(\gamma_1,\gamma_2) = \int \langle \gamma_1(\theta), \gamma'_2(\theta)\rangle d\theta \end{equation} where $\langle \cdot,\cdot\rangle$ is left-action invariant bilinear form on $L\mathfrak{g}$. The question is: is there a similar and --more important-- explicit (as much as possible) formula for the 2-co-cycle on $LG$. | |
| Mar 7, 2012 at 10:14 | comment | added | Konrad Waldorf | Could you please clarify what you mean by 2-cocycles on a loop group? Do you mean a smooth map $LG \times LG \to A$ satisfying the cocycle condition? What is $A$? | |
| Mar 7, 2012 at 9:01 | history | edited | Damien S. |
edited tags
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| Mar 7, 2012 at 8:35 | history | edited | Damien S. | CC BY-SA 3.0 |
added 666 characters in body; added 9 characters in body
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| Mar 6, 2012 at 16:19 | answer | added | André Henriques | timeline score: 3 | |
| Mar 6, 2012 at 16:00 | history | edited | Damien S. | CC BY-SA 3.0 |
edited title
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| Mar 6, 2012 at 15:53 | history | asked | Damien S. | CC BY-SA 3.0 |