Timeline for Outer automorphisms of simple Lie Algebras
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 24, 2014 at 22:55 | comment | added | Torsten Schoeneberg | A good account of the outer and inner automorphisms of a semisimple LA is ch. VIII § 5 of Bourbaki's Lie Groups and Lie Algebras. (It is in the more general setting of a split semisimple LA over a field of char. 0.) At the end of no. 2 there is a beautiful diagram which not only gives $Out(\mathfrak{g}) \simeq Aut(R)/W(R)$ (=$Aut$(Dynkin diagram)), but also addresses the "extension problem" Jason DeVito alludes to. | |
| Jul 17, 2011 at 22:47 | answer | added | HilbertsGreatgrandchild | timeline score: 8 | |
| May 4, 2011 at 12:36 | comment | added | Zoran Skoda | This is well known for Lie algebras. How about the outer automorphisms of real simple Lie groups ? | |
| Feb 10, 2010 at 0:36 | vote | accept | blt | ||
| Feb 9, 2010 at 15:10 | answer | added | Allen Knutson | timeline score: 7 | |
| Feb 9, 2010 at 14:28 | comment | added | Jason DeVito - on hiatus | @Vladimir - Of course! That's what I get for doing math too late. Thank you! | |
| Feb 9, 2010 at 9:13 | comment | added | Vladimir Dotsenko | Jason, you must be kidding. Out=Aut/Inn is the automorphism group of the Dynkin diagram. | |
| Feb 9, 2010 at 5:29 | answer | added | Steven Sam | timeline score: 27 | |
| Feb 9, 2010 at 5:25 | answer | added | Theo Johnson-Freyd | timeline score: 12 | |
| Feb 9, 2010 at 5:15 | comment | added | Jason DeVito - on hiatus | Out/Inn is isomorphic to the automorphism group of the Dynkin diagram. There are potential extension problems for recovering Out from this data, though. | |
| Feb 9, 2010 at 4:48 | comment | added | Emerton | Is an ``inner automorphism'' of the Lie algebra an automorphism coming from the adjoint action of the associated simple complex Lie group? If so, then aren't the outer automorphisms given by automorphisms of the Dynkin diagram? | |
| Feb 9, 2010 at 3:31 | history | asked | blt | CC BY-SA 2.5 |