Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Alfons OOMS - ,
Titre On the polynomiality of the Poisson center and semi-center of a Lie algebra of index at most two
Horaire14:00 à 15:00
RésumeLet L be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero and let S(L) be its symmetric algebra, equipped with its natural Poisson structure. L is called coregular if the Poisson center of S(L) is polynomial. We collect some simple criteria in order for this to occur. Examples show that this happens very rarely when the index of L is rather large, compared to the dimension of L. Therefore it seems natural to let the index be at most two. Under this condition any nilpotent Lie algebra is coregular. This result is not true in the solvable case or if the index is equal to three. On the other hand, any nonsolvable Lie algebra of dimension at most eight is coregular. A counterexample is given in dimension nine.