Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I was told that a polynomial group law on (all of) $\mathbb{R}^n$ gives automatically a nilpotent (Lie, of course) group.

Is it true? Where can I find a proof?

A counterexample for open subsets of $\mathbb{R}^n$ is furnished by the halfplane with the $ax+b$ law.

share|improve this question
1  
Torsten, make it an answer (not just a comment). –  Sammy Black Apr 17 '10 at 19:13
    
Thank you, Torsten! –  Gian Maria Dall'Ara Apr 17 '10 at 19:49
    
Moved a comment to an answer as per instructions. –  Torsten Ekedahl Apr 17 '10 at 20:36

1 Answer 1

up vote 15 down vote accepted

This is true and is in "Michel Lazard: Sur la nilpotence de certains groupes algébriques, Comptes Rendus, vol 241, 1955, 1687--1689"

share|improve this answer
2  
This short paper is apparently not available online, but a version of Lazard's theorem is also written down in the 1970 book by Demazure-Gabriel, Groupes algebriques, I: see IV, section 4, 4.1. –  Jim Humphreys Apr 17 '10 at 20:53

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.