Let g be a real semisimple Lie algebra with Killing form B and k a B-nondegenerate subalgebra of g of maximal rank. We give a description of all ad_k-invariant decompositions g = k + m^+ + m^- such that B|_m^\± = 0, B(k,m^+ + m^-) = 0 and k + m^\± are subalgebras. It is reduced to a description of parabolic subalgebras of g with given reductive part k. This is obtained in terms of crossed Satake diagrams. As an application, we get a classification of invariant bi-Lagrangian (or equivalently para-Kähler) structures on homogeneous manifolds G/K of a semisimple group G.

Bi-isotropic decompositions of semisimple Lie algebras and homogeneous bi-Lagrangian manifolds / D. V., Alekseevsky; Medori, Costantino. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 313:1(2007), pp. 8-27. [10.1016/j.jalgebra.2006.11.038]

Bi-isotropic decompositions of semisimple Lie algebras and homogeneous bi-Lagrangian manifolds

MEDORI, Costantino
2007

Abstract

Let g be a real semisimple Lie algebra with Killing form B and k a B-nondegenerate subalgebra of g of maximal rank. We give a description of all ad_k-invariant decompositions g = k + m^+ + m^- such that B|_m^\± = 0, B(k,m^+ + m^-) = 0 and k + m^\± are subalgebras. It is reduced to a description of parabolic subalgebras of g with given reductive part k. This is obtained in terms of crossed Satake diagrams. As an application, we get a classification of invariant bi-Lagrangian (or equivalently para-Kähler) structures on homogeneous manifolds G/K of a semisimple group G.
Bi-isotropic decompositions of semisimple Lie algebras and homogeneous bi-Lagrangian manifolds / D. V., Alekseevsky; Medori, Costantino. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 313:1(2007), pp. 8-27. [10.1016/j.jalgebra.2006.11.038]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/1642726
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