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Nambu-Poisson tensors on Lie groups. (English) Zbl 0966.53053
Grabowski, Janusz (ed.) et al., Poisson geometry. Stanisław Zakrzewski in memoriam. Warszawa: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 51, 243-249 (2000).
A Nambu-Poisson structure on a manifold can be defined by a \(k\)-vector field satisfying an integrability condition. If \(k=2\) the Nambu-Poisson structures coincide with Poisson structures. The author first gives a characterization of Nambu-Poisson structures in terms of forms rather than \(k\)-vector fields provided the manifold is endowed with a volume form. Next a description of left invariant Nambu-Poisson tensors on a Lie group in terms of subalgebras of the corresponding Lie algebra is presented. It is also studied under what conditions Nambu-Poisson tensors could be projected onto the corresponding homogeneous space.
For the entire collection see [Zbl 0936.00035].

MSC:
53D17 Poisson manifolds; Poisson groupoids and algebroids
53C30 Differential geometry of homogeneous manifolds
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