Timeline for What is the importance of Cartan decomposition of a semi-simple Lie algebra?
Current License: CC BY-SA 4.0
6 events
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| Jun 19, 2022 at 13:56 | comment | added | Callum | Just so people who arrive here know about it, I've posted an answer over on the stack exchange post. | |
| Jun 17, 2022 at 3:32 | comment | added | Mikhail Borovoi | which shows that the group is homotopy equivalent to a maximal compact subgroup. | |
| Jun 17, 2022 at 3:30 | comment | added | Mikhail Borovoi | Maybe because, using a Cartan decomposition of the Lie algebra of a real semisimple Lie group, we obtain a Cartan decomposition of the group, | |
| Jun 16, 2022 at 22:45 | comment | added | Sam Hopkins | (In fact, IIRC the existence of a Cartan subalgebra is the one small fact that Killing did not fully prove in his original proof of the classification of simple Lie algebras, although the proof is not difficult.) | |
| Jun 16, 2022 at 22:40 | comment | added | Sam Hopkins | Certainly the existence of a Cartan subalgebra is used in the usual proof of the classification of simple Lie algebras. I'm not sure if the whole Cartan decomposition is necessary for that; but it is useful for classification the representations at least. | |
| Jun 16, 2022 at 22:22 | history | asked | Mira | CC BY-SA 4.0 |