Timeline for analytic structure on lie groups
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2013 at 16:46 | answer | added | Peter Michor | timeline score: 5 | |
| Apr 21, 2013 at 14:48 | history | edited | user9072 |
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| Apr 12, 2011 at 21:37 | answer | added | Enrique Macias | timeline score: 3 | |
| Dec 17, 2010 at 6:31 | comment | added | faquarl | was not quite aware that was how the latter statement read...thanx.. | |
| Dec 16, 2010 at 1:37 | answer | added | MTS | timeline score: 2 | |
| Dec 16, 2010 at 1:11 | comment | added | BCnrd | With suitable analytic foundations (including real-analytic Frobenius-integrability!) the entire development of elementary Lie theory works in the real-analytic category verbatim, up to and including the fact that the functor from a (connected and) simply connected Lie group (either smooth or real-analytic) to its Lie algebra is an equivalence of categories. So comparison through the Lie algebras does the job. Can be seen in more direct ways too (e.g., using graph arguments and real-analytic Frobenius-integrability). | |
| Dec 16, 2010 at 1:03 | comment | added | BCnrd | These statements are entirely different: first involves functoriality, 2nd concerns objects up to isomorphism. The forgetful functor from real-an. Lie groups to smooth Lie groups is an equivalence of categories, whereas the functor from (paracompact) real-an. manifolds to (paracompact) smooth manifolds is merely essentially surjective on objects (Morrey-Grauert) and bijective between isomorphism classes. It is much weaker to say that smoothly isomorphic real-an. mnflds are analytically isom. than to say that some smooth isom. is real-an. (or that all smooth maps are real-an.). | |
| Dec 16, 2010 at 0:56 | history | asked | faquarl | CC BY-SA 2.5 |