Timeline for Lie algebras and complements
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 16, 2010 at 13:42 | comment | added | student | Are there special names in the literature for the situations in 1) and 2) I mentioned ? I have found something about 2), if the lie-Algebras arise as Lie-Algebras of some connected Lie-Groups, $G$ resp. $G_1$ ($G_1$ normal Lie-subgroup in $G$), having a vector space complement $\mathfrak{g}_2$ with $[\mathfrak{g}_1,\mathfrak{g}_2] = 0$ means that $\mathfrak{g}_2$ ist $G_1$-invariant. And such a homogenous space $G/G_1$ is called reductive, I have found that in O'Neill, Semi-Riemannian-Geometry and Baums "Eichfeldtheorie" book. But I havn't found any more comprehensive references. | |
| Jul 13, 2010 at 16:56 | comment | added | Theo Johnson-Freyd | @Jim: JFF's answer below is not (very) dependent on the choice of field. | |
| Jul 13, 2010 at 12:33 | comment | added | student | As a base field I want the real numbers or the complex numbers. | |
| Jul 13, 2010 at 11:45 | comment | added | Jim Humphreys | For this kind of question, it's important to specify the base field and whether it is algebraically closed. | |
| Jul 13, 2010 at 11:05 | answer | added | José Figueroa-O'Farrill | timeline score: 12 | |
| Jul 13, 2010 at 10:11 | history | edited | Charles Matthews | CC BY-SA 2.5 |
copy edit
|
| Jul 13, 2010 at 10:07 | history | asked | student | CC BY-SA 2.5 |