Timeline for Applications of Govorov-Lazard Theorem?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Jul 16, 2014 at 18:47 | comment | added | Charles Rezk | @Ralph: The "equational criterion" can be stated approximately as follows: $M$ is flat iff any map to it from a finitely presented module $N$ factors through a f.g. free module. (The statement of the equational criterion that I usually see is what you get if you rewrite what I just said in terms of the finite presentation $R^p\to R^q$ of $N$, instead of $N$ itself, which can then be written in terms of solving some linear systems of linear equations with variables in $R$ and $M$.) | |
| May 5, 2013 at 8:08 | answer | added | Martin Brandenburg | timeline score: 3 | |
| May 2, 2013 at 21:34 | vote | accept | Ralph | ||
| Apr 18, 2013 at 15:47 | answer | added | David White | timeline score: 7 | |
| Apr 17, 2013 at 22:50 | comment | added | darij grinberg | Ralph: I hesitated to post it as answer exactly because I wasn't sure whether Higgins ever used it. Weirdly enough, the flat version of PBW appeared on Wikipedia, with reference to Higgins... Someone's been doing original research, apparently :) | |
| Apr 17, 2013 at 19:11 | comment | added | Ralph | @darij: As far as I can see, L-G is neither used in Higgins paper nor does Higgins treat the flat case. If I'm not missing something this is quite surprising because the flat case follows immediately from Higgins results and L-G. Higgins paper was submitted 1968 while the paper from Govorov was published 1965 and that of Lazard 1969. So it unclear, if Higgins should had known L-G when he was writing his paper. In any case L-G is an interesting application on the flat Birkhoff-Witt. Wouldn't you like to post this as an answer ? | |
| Apr 17, 2013 at 18:35 | comment | added | Ralph | @James: What is the equational criterion ? | |
| Apr 17, 2013 at 9:15 | comment | added | JBorger | Closely related to the G-L theorem is the equational criterion for flatness, which I really like. It provides a nice counterpoint to the more common category-theoretic or homological points of view on flatness. | |
| Apr 17, 2013 at 8:37 | answer | added | Olivier | timeline score: 10 | |
| Apr 17, 2013 at 4:05 | answer | added | user30180 | timeline score: 3 | |
| Apr 17, 2013 at 1:48 | comment | added | darij grinberg | (Probably it's part of the proof that Poincaré-Birkhoff-Witt itself, not just some relative version, holds for Lie algebras which are flat as modules over the base ring. I have not studied this proof but I think it should be in P. J. Higgins, Baer Invariants and the Birkhoff-Witt Theorem, Journal of Algebra 11, pp. 469-482 (1969).) | |
| Apr 17, 2013 at 1:45 | comment | added | darij grinberg | YMMV on whether this is interesting, but it helps generalize some relative version of Poincaré-Birkhoff-Witt to Lie algebras which are flat as modules over rings: mathoverflow.net/questions/65675/… | |
| Apr 16, 2013 at 23:16 | history | asked | Ralph | CC BY-SA 3.0 |