On Riemann-Poisson Lie groups. (English) Zbl 1524.53170

A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor satisfying a compatibility condition. Such groups belong to the family of Riemann-Poisson manifolds introduced and studied by the second author in several publications. In this paper, the authors study these Lie groups and present a characterization of their Lie algebras. Moreover, a way of building these Lie algebras is given and a list up to dimension 5 is given.


53D17 Poisson manifolds; Poisson groupoids and algebroids
22E05 Local Lie groups
22E60 Lie algebras of Lie groups
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