Timeline for Nice proofs of the Poincaré–Birkhoff–Witt theorem
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2018 at 6:03 | comment | added | Martin Sleziak | The link to Emanuale Petracci's thesis in the post seems to be that, but it is available in Internet Archive. | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Feb 5, 2013 at 23:40 | comment | added | Johannes Ebert | Lie's Third Theorem is hard, but there is a wonderful differential geometric proof whose Lie algebraic part is really simple. I found it in a paper by Van Est, "Une demonstration de E. Cartan du troisieme theoreme de Lie". Another proof of Lie III without even less Lie algebra theory is in the book by Duistermaat-Kolk. Both proofs use that $H^2(G;\mathbb{R})=0$ for simply-connected Lie group. | |
| Feb 5, 2013 at 14:23 | history | edited | darij grinberg | CC BY-SA 3.0 |
added 56 characters in body
|
| Feb 5, 2013 at 9:35 | comment | added | M T | A nice feature of the Cartan-Eilenberg proof pointed out by Mariano is that it works for Lie algebras which are free over an arbitrary commutative ring. | |
| Feb 11, 2012 at 4:18 | comment | added | Mariano Suárez-Álvarez | The book by Cartan and Eilenberg includes a nice, straightforward proof. | |
| Feb 3, 2012 at 11:39 | comment | added | Pierre-Yves Gaillard | It seems to me that the paper "The diamond lemma for ring theory", Advances in Mathematics 29 (1978) 178-218, by George M. Bergman has not been quoted in this thread. Related link: math.berkeley.edu/~gbergman/papers/updates/diamond.html | |
| Feb 3, 2012 at 11:26 | comment | added | darij grinberg | Oh right. How did I forget about that one... | |
| Feb 3, 2012 at 11:08 | comment | added | Vladimir Dotsenko | @Damien: I already mentioned this article in a comment to the original post ;-) | |
| Feb 3, 2012 at 10:57 | comment | added | DamienC | There is also a nice homological/deformation theoretic proof by Braverman and Gaitsgory: arxiv.org/abs/hep-th/9411113 ("The Poincare-Birkhoff-Witt theorem for quadratic algebras of Koszul type"). | |
| Feb 3, 2012 at 9:48 | history | answered | darij grinberg | CC BY-SA 3.0 |