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) Ryosuke KODERA - Tokyo,
Titre $Ext^1$ for simple modules over $U_q(L\mathfrak{sl}_2)$
Horaire15:30 à 16:30
RésumeI talk about a partial result on the calculation of the Ext groups for finite-dimensional simple modules over the quantum loop algerba $U_q(L\mathfrak{sl}_2)$. In particular, the finite-dimensional simple modules that admit nontrivial extensions between the trivial module are determined. I also discuss a refinement of a recent result by Chari-Moura-Young \href{http://arxiv.org/abs/1112.6376}{arXiv:1112.6376}, which establishes a relation between the dimension of the self-extension group and the number of factors in the prime factorization for a simple $U_q(L\mathfrak{sl}_2)$-module.