On local structure of pseudo-Riemannian Poisson manifolds and pseudo-Riemannian Lie algebras (Q2905190)
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scientific article; zbMATH DE number 6072206
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On local structure of pseudo-Riemannian Poisson manifolds and pseudo-Riemannian Lie algebras |
scientific article; zbMATH DE number 6072206 |
Statements
24 August 2012
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Levi decomposition
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pseudo-Riemannian Poisson manifold
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pseudo-Riemannian Lie algebra
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math.RA
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On local structure of pseudo-Riemannian Poisson manifolds and pseudo-Riemannian Lie algebras (English)
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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.
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0.8564530611038208
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0.8502623438835144
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0.8020991086959839
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0.8020991086959839
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0.7672175168991089
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