Lie algebroids associated to Poisson actions
نویسنده
چکیده
Let P be a Poisson homogeneous G-space. In [Dr2], Drinfeld shows that corresponding to each p ∈ P , there is a maximal isotropic Lie subalgebra lp of the Lie algebra d, the double Lie algebra of the tangent Lie bialgebra (g, g∗) of G. Moreover, for g ∈ G, the two Lie algebras lp and lgp are related by lgp = Adg lp via the Adjoint action of G on d. In particular, they are isomorphic as Lie algebras. The Lie algebra lp determines the Poisson structure on P , and it can be used to classify Poisson homogeneous G-spaces [Dr2].
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