Address:
a Université de Nouakchott, Faculté des sciences et techniques
b Université Cadi-Ayyad, Faculté des sciences et techniques, BP 549 Marrakech Maroc
c Université de Nouakchott, Faculté des sciences et techniques
E-mail:
pacha.ali86@gmail.com
m.boucetta@uca.ac.ma
lessiadahmed@gmail.com
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 [4]. 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.
AMSclassification: primary 53A15; secondary 53D17, 22E05.
Keywords: Lie group, Poisson manifolds, Riemannian metric.
DOI: 10.5817/AM2020-4-225