On the Riemann-Lie Algebras and Riemann-Poisson Lie Groups

Mohamed Boucetta

Abstract: A Riemann-Lie algebra is a Lie algebra $\cal G$ such that its dual ${\cal G}^*$ carries a Riemannian metric compatible (in the sense introduced by the author in C. R. Acad. Sci. Paris, 333, Série I, (2001) 763–768) with the canonical linear Poisson structure of ${\cal G}^*$. The notion of Riemann-Lie algebra has its origins in the study, by the author, of Riemann-Poisson manifolds (see Differential Geometry and its Applications, 20 (2004), 279–291).

Full text of the article: (for faster download, first choose a mirror)

• PDF file (172 kilobytes)