no. 1-2
Lie Algebras
Generalized flag geometries and manifolds associated to short Z-graded Lie algebras in arbitrary dimension
[Géométries de drapeaux généralisées et variétés associées aux algèbres de Lie graduées en dimension quelconque]

Présenté par : Michèle Vergne

Chenal, Julien1
1 Institut Elie-Cartan Nancy (IECN), Nancy-Université, CNRS, INRIA, boulevard des Aiguillettes, B.P. 239, 54506 Vandoeuvre-lès-Nancy, France
Comptes Rendus. Mathématique, Tome 347 (2009) no. 1-2, pp. 21-25.

L'objet de cette Note est de définir la géométrie de drapeaux généralisée d'une algèbre de Lie graduée, qui correspond à la géométrie projective généralisée dans le cas des 3-graduations, puis de construire une structure de variété différentielle sur cette géométrie. Ce résultat généralise au cas des (2k+1)-graduations un résultat déjà connu pour les 3-graduations.

The object of this Note is to define the generalized flag geometry of a graded Lie algebra which corresponds to the generalized projective geometry in the case of 3-gradings. Then we construct a structure of manifold on this generalized flag geometry. This result generalizes a result known for 3-graded Lie algebras to the more general case of (2k+1)-graded Lie algebras.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.12.001
Chenal, Julien 1

1 Institut Elie-Cartan Nancy (IECN), Nancy-Université, CNRS, INRIA, boulevard des Aiguillettes, B.P. 239, 54506 Vandoeuvre-lès-Nancy, France 
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Chenal, Julien. Generalized flag geometries and manifolds associated to short $ \mathbb{Z}$-graded Lie algebras in arbitrary dimension. Comptes Rendus. Mathématique, Tome 347 (2009) no. 1-2, pp. 21-25. doi : 10.1016/j.crma.2008.12.001. http://www.numdam.org/articles/10.1016/j.crma.2008.12.001/

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