Timeline for What are "classical groups"?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Dec 6, 2011 at 5:19 | comment | added | Will Sawin | The infinite-dimensional case seems apparently ambiguous, so it's probably best not to use it in deciding between definitions. Or one could just add ("in infinite dimensions, it means ....") to the end of the definition. | |
| Feb 16, 2011 at 9:54 | comment | added | Tom De Medts | So what about, for example, O(V,q), where q is a quadratic form on some infinite-dimensional vector space V? I would call such a group classical, but it doesn't even have a Dynkin diagram... | |
| Dec 30, 2010 at 3:05 | comment | added | Allen Knutson | I have definitely heard it claimed that $SO(n)$ is not a classical group -- only $O(n)$ is. This may have been by someone partial to the Porteous result (I actually can't remember who it was). | |
| Dec 29, 2010 at 19:18 | comment | added | José Figueroa-O'Farrill | All I meant was that all Lie groups having the same Dynkin diagram, have the same Lie algebra. So your answer seemed to me saying that you define a notion of classical Lie algebra to be a simple Lie algebra of type A,B,C or D; and then a classical Lie group is one whose Lie algebra is classical. | |
| Dec 29, 2010 at 18:26 | comment | added | Richard Borcherds | I don't understand this comment, as my answer did not mention Lie algebras. | |
| Dec 29, 2010 at 5:52 | comment | added | José Figueroa-O'Farrill | So what you seem to be saying is that one should talk about classical Lie algebras instead of classical Lie groups. | |
| Dec 29, 2010 at 5:17 | history | answered | Richard Borcherds | CC BY-SA 2.5 |