Timeline for Using topology to characterize embedded Lie subgroups of Lie groups.
Current License: CC BY-SA 2.5
6 events
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| Mar 1, 2010 at 0:45 | history | edited | José Figueroa-O'Farrill | CC BY-SA 2.5 |
added 159 characters in body
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| Mar 1, 2010 at 0:44 | comment | added | José Figueroa-O'Farrill | Fair enough. My answer is then not relevant. Sorry! | |
| Feb 28, 2010 at 19:13 | comment | added | Khalid Bou-Rabee | I added "embedded" in front of Lie subgroup. The reason why I ask this is because I am curious of whether there are other versions of Cartan's theorem. | |
| Feb 28, 2010 at 16:33 | comment | added | José Figueroa-O'Farrill | Why would you want to rule out the irrationally sloped lines on the torus? They are perfectly good Lie subgroups. In fact, you don't get a good version of the inverse Lie correspondence unless you take such subgroups into account. The lesson from Chevalley's work, in my opinion, is that demanding that the subgroups be embedded submanifolds is too restrictive. | |
| Feb 28, 2010 at 16:02 | comment | added | Khalid Bou-Rabee | Thank you for your post. I am asking for another form of Cartan's theorem. Let H be a subgroup of a Lie group G. In Cartan's theorem the topological property, closed, refers to H with the subset topology from G. I am not asking for you to invent a new topology (I ruled out irrationally sloped lines on a flat torus, which are analytic subgroups but not Lie subgroups). Recall that stating that H is Lie subgroup of G means more than just that H is a Lie group that is also a subgroup of G. Please see the wikipedia article en.wikipedia.org/wiki/Lie_subgroup for a complete definition. | |
| Feb 28, 2010 at 2:22 | history | answered | José Figueroa-O'Farrill | CC BY-SA 2.5 |