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Alioune, Brahim; Boucetta, Mohamed; Sid’Ahmed Lessiad, Ahmed

On Riemann-Poisson Lie groups. (English) Zbl 07285962

Arch. Math., Brno 56, No. 4, 225-247 (2020).
Summary: A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in [M. Boucetta, Differ. Geom. Appl. 20, No. 3, 279–291 (2004; Zbl 1061.53058)]. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.

MSC:

53A15 Affine differential geometry
53D17 Poisson manifolds; Poisson groupoids and algebroids
22E05 Local Lie groups

Keywords:

Lie group; Poisson manifolds; Riemannian metric

Citations:

Zbl 1061.53058
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\textit{B. Alioune} et al., Arch. Math., Brno 56, No. 4, 225--247 (2020; Zbl 07285962)
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References:

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