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Paramétrisation du dual d'une algèbre de Lie nilpotente

Pierre Bonnet (1988)

Annales de l'institut Fourier

Pour tout groupe de Lie nilpotent réel G connexe et simplement connexe, on construit une stratification du dual de l’algèbre de Lie, et on paramètre chaque strate au moyen d’un triplet ( λ , q , p ) de fonctions rationnelles à valeurs vectorielles; les valeurs de λ caractérisent les orbites de la strate et pour chacune de ces orbites, le couple ( q , p ) constitue une carte de Darboux.

Partial flag varieties and preprojective algebras

Christof Geiß, Bernard Leclerc, Jan Schröer (2008)

Annales de l’institut Fourier

Let Λ be a preprojective algebra of type A , D , E , and let G be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories Sub Q for Q an injective Λ -module, and we introduce a mutation operation between complete rigid modules in Sub Q . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to  G .

Poincaré’s proof of the co-called Birkhoff-Witt theorem

Tuong Ton-That, Thai-Duong Tran (1999)

Revue d'histoire des mathématiques

A methodical analysis of the research related to the article, “Sur les groupes continus”, of Henri Poincaré reveals many historical misconceptions and inaccuracies regarding his contribution to Lie theory. A thorough reading of this article confirms the priority of his discovery of many important concepts, especially that of the universal enveloping algebra of a Lie algebra over the real or complex field, and the canonical map (symmetrization) of the symmetric algebra onto the universal enveloping...

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