EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 15, No. 1, pp. 183–195 (2005)

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

Mohamed Boucetta

M. Boucetta
FacultÚ des sciences et techniques Gueliz
BP 549 Marrakech Morocco
boucetta@fstg-marrakech.ac.ma

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, SÚrie 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).

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