Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Benoît Stroh
Email des responsables : alexis.bouthier@imj-prg.fr, benoit.stroh@imj-prg.fr
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Orateur(s) Hans-Jürgen SCHNEIDER - ,
Titre On the alternating square of a Lie algebra
Date24/02/2011
Horaire14:00 à 15:00
Diffusion
RésumeThe Lie bracket of a Lie algebra $L$ induces a linear map $L \wedge L \rightarrow L$. When can the kernel of this map be generated by vectors of the form $x \wedge y$ with $[x,y]=0$? This seemingly elementary question does not seem to be tractable by elementary methods. For semisimple Lie algebras over the complex numbers Kostant has given a positive answer by means of representation theory. I will explain why a number theorist is interested in this question over fields of positive characteristics. I will sketch a solution for the Chevalley form of any split semisimple Lie algebra (joint work with O. Venjakob).
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