Generalized flag geometries and manifolds associated to short Z-graded Lie algebras in arbitrary dimension.

Julien Chenal (1)

1 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: Graded Lie algebras; Projective elementary group; Generalized flag geometry

Domaines: Anneaux et algèbres [math.RA]

Julien Chenal. Generalized flag geometries and manifolds associated to short Z-graded Lie algebras in arbitrary dimension.. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2009, 347, pp.21-25. ⟨10.1016/j.crma.2008.12.001⟩. ⟨hal-00435859⟩