On Local Structure of Pseudo-Riemannian Poisson Manifolds and Pseudo-Riemannian Lie Algebras
Copyright policy )On Local Structure of Pseudo-Riemannian Poisson Manifolds and Pseudo-Riemannian Lie Algebras
The results of the paper under review are related to the work of \textit{M. Boucetta} [C. R. Acad. Sci., Paris, Sér. I, Math. 333, No. 8, 763--768 (2001; Zbl 1009.53057); Differ. Geom. Appl. 20, No. 3, 279--291 (2004; Zbl 1061.53058); J. Lie Theory 15, No. 1, 183--195 (2005; Zbl 1077.53065)], on the compatibility between pseudo-Riemannian structures and Poisson structures, Poisson Lie groups, and Lie algebras. Alternative proofs of these results are proposed, and one also proves that the pseudo-Riemannian Lie algebras are solvable.
Poisson manifolds; Poisson groupoids and algebroids, Solvable, nilpotent (super)algebras, pseudo-Riemannian Lie algebra, Levi decomposition, pseudo-Riemannian Poisson manifold
Poisson manifolds; Poisson groupoids and algebroids, Solvable, nilpotent (super)algebras, pseudo-Riemannian Lie algebra, Levi decomposition, pseudo-Riemannian Poisson manifold
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