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Outer endomorphisms of free metabelian Lie algebras

Findik, Sehmus (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.Let Fm be the free metabelian Lie algebra of rank m over a field K of characteristic 0. We consider the semigroup IE(Fm) of the endomorphisms of Fm which are identical modulo the commutator ideal of Fm. We describe the factor semigroup of IE(Fm) modulo the congruence induced by the group of inner automorphisms.

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 .

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