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

JOURNAL OF ALGEBRA

卷:313

Article

Alekseevsky, Dmitri V. ; Medori, Costantino

关键词: homogeneous space;    pseudo-Riemannian manifold;    symplectic manifold;    Para-Kaehler manifold;    bi-Lagrangian structure;   

DOI  :  10.1016/j.jalgebra.2006.11.038

来源: Elsevier

【 摘 要 】

Let g be a real semisimple Lie algebra with Killing form B and t a B-nondegenerate subalgebra of g of maximal rank. We give a description of all ad(t)-invariant decompositions g = f + m(+) + m(-) such that B vertical bar(m)+/- = 0, B (t, m(+) + m(-)) = 0 and t + m(+/-) are subalgebras. It is reduced to a description of parabolic subalgebras of g with given reductive part t. This is obtained in terms of crossed Satake diagrams. As an application, we get a classification of invariant bi-Lagrangian (or equivalently para-Kuhler) structures on homogeneous manifolds G/K of a semisimple group G. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free