Timeline for How do you recover the structure of the upper half plane from its description as a coset space?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2010 at 21:58 | comment | added | José Figueroa-O'Farrill | The adjoint representation of O(2,1) on its Lie algebra preserves the Killing form, which has signature (2,1). This is as canonical as it gets. This is very particular to this signature, though. | |
| Mar 29, 2010 at 21:05 | comment | added | Charlie Frohman | Yes, if you include the structure of Lie algebras as part of your group theoretic things. When I was a student I really enjoyed Helgason's Differential Geometry, Lie Groups and Symmetric Spaces, and Joe Wolfe's Spaces of Constant Curvature. | |
| Mar 29, 2010 at 20:49 | comment | added | Qiaochu Yuan | I guess I'm not explaining myself well. Suppose I'm given a nice topological group G and a nice subgroup H. Then G/H is a topological space. What are general situations in which G/H comes equipped with extra geometric structure, and how much about G and H do I have to know to find that structure? (In other words, is it enough to have a black box which tells you group-theoretic things about G and H such as their other subgroups?) | |
| Mar 29, 2010 at 20:00 | comment | added | Tom Church | What is O(2,1) except the linear isometries of Minkowski space? | |
| Mar 29, 2010 at 18:33 | comment | added | Qiaochu Yuan | I like this explanation very much - I remember Scott Carnahan explaining this to us once - but one has to produce the action of O(2, 1) on a "unit ball" in order to do this. Given only the abstract structure of O(2, 1) (in whatever category is necessary), can one recover its action on Minkowski space? | |
| Mar 29, 2010 at 18:23 | history | edited | José Figueroa-O'Farrill | CC BY-SA 2.5 |
added 273 characters in body
|
| Mar 29, 2010 at 18:18 | history | answered | José Figueroa-O'Farrill | CC BY-SA 2.5 |