English

On Riemann-Poisson Lie groups

Differential Geometry 2019-08-15 v1 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.1908.05060,
  title  = {On Riemann-Poisson Lie groups},
  author = {Brahim Alioune and Mohamed Boucetta and Ahmed Sid'Ahmed Lessiad},
  journal= {arXiv preprint arXiv:1908.05060},
  year   = {2019}
}

Comments

23 pages, submitted

R2 v1 2026-06-23T10:47:16.748Z