Timeline for Does a finite-dimensional Lie algebra always exponentiate into a universal covering group
Current License: CC BY-SA 2.5
9 events
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| Oct 10, 2010 at 21:00 | history | edited | Greg Kuperberg | CC BY-SA 2.5 |
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| Oct 10, 2010 at 20:59 | comment | added | Greg Kuperberg | BLech, I meant PSL(2) is double covered by SL(2). | |
| Oct 10, 2010 at 20:39 | comment | added | Theo Johnson-Freyd | scratches head The double cover of SL(2,R) has a finite-dimensional representation? I was under the impression that the following was true: any representation of a cover of SL(2,R) is determined by the action of sl(2,R); we know the full finite-dimensional representation theory of sl(2,R); all representations integrate to representations of SL(2,R). At least, that's the impression that R. Borcherds gave in the notes I've linked to. Let me know if there's an error --- the notes are still in draft form. | |
| Oct 10, 2010 at 11:57 | comment | added | Greg Kuperberg | There, maybe I fixed it now. | |
| Oct 10, 2010 at 11:57 | history | edited | Greg Kuperberg | CC BY-SA 2.5 |
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| Oct 10, 2010 at 11:11 | comment | added | Greg Kuperberg | No, actually there is a bug in what I'm saying. I'm fudging the difference between a complex representation of a complex Lie group and a real representation of a complex Lie group. I'll have to think of the best way to clarify the answer, although in the last paragraph I may have meant, every simply connected complex Lie group. | |
| Oct 10, 2010 at 10:54 | comment | added | S. Carnahan♦ | I was about to say that abelian varieties are complex Lie groups that do not have faithful finite dimensional representations, but now I think we may be using different definitions of "representation". | |
| Oct 10, 2010 at 9:57 | history | edited | Greg Kuperberg | CC BY-SA 2.5 |
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| Oct 10, 2010 at 7:59 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |