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arXiv · 1908.05060

On Riemann-Poisson Lie groups

Brahim Alioune·Mohamed Boucetta·Ahmed Sid'Ahmed Lessiad
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Abstract

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 C.R. Acad. Sci. Paris s\'er. {\bf I 333} (2001) 763-768. 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.

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Brahim Alioune, Mohamed Boucetta, Ahmed Sid'Ahmed Lessiad. 2019-08-14. On Riemann-Poisson Lie groups. https://arxiv.org/abs/1908.05060

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