Timeline for Is it possible to construct a formal group law from a Lie group without choosing coordinates?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Oct 22, 2013 at 9:22 | vote | accept | Richard Garner | ||
| Oct 22, 2013 at 9:01 | comment | added | David Roberts♦ | Hi Richard, congrats on your first MO contribution! :-) | |
| Oct 22, 2013 at 7:31 | answer | added | Marguax | timeline score: 10 | |
| Oct 22, 2013 at 7:12 | answer | added | Qiaochu Yuan | timeline score: 17 | |
| Oct 22, 2013 at 3:05 | history | edited | Richard Garner | CC BY-SA 3.0 |
added 33 characters in body
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| Oct 22, 2013 at 3:04 | comment | added | Richard Garner | Thanks, Peter. You're right that (1) and (2) are not in correspondence in quite the form I stated. Have edited. As to your other comment, that is illuminating; really what is happening is that the equivalence between the categories of Lie algebras and formal group laws is only canonically defined in the direction from the latter to the former; the converse requires the axiom of choice (a choice of basis for each Lie algebra). | |
| Oct 22, 2013 at 2:59 | comment | added | Drew Heard | Maybe the answer is to look at formal groups (as opposed to formal group laws)? | |
| Oct 22, 2013 at 2:48 | comment | added | Peter Crooks | Also, I do not think passage from the first to the second is a correspondence. In general, there are many non-isomorphic Lie groups with a given (isomorphism class of) Lie algebra. If you require your Lie groups to be connected and simply-connected, then taking Lie algebras gives a correspondence. | |
| Oct 22, 2013 at 1:58 | comment | added | Peter Crooks | It would seem that passage from the second to the third involves a choice of basis for your Lie algebra. Since the exponential map is a local diffeomorphism, this choice of basis is essentially a choice of local coordinates at the identity of the group (and hence elsewhere). So, it looks like a choice of coordinates arises in other places. | |
| Oct 22, 2013 at 0:06 | review | First posts | |||
| Oct 22, 2013 at 0:20 | |||||
| Oct 21, 2013 at 23:54 | history | edited | Richard Garner | CC BY-SA 3.0 |
edited title
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| Oct 21, 2013 at 23:46 | history | asked | Richard Garner | CC BY-SA 3.0 |