We show in this paper that the tangent bundle T G, of a Poisson-Lie group G has a Poisson-Lie group structure given by the canonical lifting of that of G. We determine the dual group of T G, its Lie bialgebra and its double Lie algebra. We also show that any Poisson action of G on a Poisson manifold P is lifted on a Poisson action of T G on the tanget bundle T P .
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