On the Riemann-Lie algebras and Riemann-Poisson Lie groups

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dc.creatorBoucetta, Mohamed
dc.date2003-10-18
dc.date.accessioned2026-07-07T05:02:04Z
dc.date.available2026-07-07T05:02:04Z
dc.descriptionA 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 th author in C. R. Acad. Paris, t. 333, Série I, (2001) 763-768) with the canonical linear Poisson sructure of ${\cal G}^*$. The notion of Riemann-Lie algebra has its origins in the study, by the author, of Riemann-Poisson manifolds (see Preprint math.DG/0206102 to appear in Differential Geometry and its Applications). In this paper, we show that, for a Lie group $G$, its Lie algebra $\cal G$ carries a structure of Riemann-Lie algebra iff $G$ carries a flat left-invariant Riemannian metric. We use this characterization to construct a huge number of Riemann-Poisson Lie groups (a Riemann-Poisson Lie group is a Poisson Lie group endowed with a left-invariant Riemannian metric compatible with the Poisson structure).
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0310293
dc.identifierhttp://arxiv.org/abs/math/0310293
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68911
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.titleOn the Riemann-Lie algebras and Riemann-Poisson Lie groups
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