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- W25207068 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 th author in C. R. Acad. Paris, t. 333, S'erie 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)." @default.
- W25207068 created "2016-06-24" @default.
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- W25207068 date "2003-10-18" @default.
- W25207068 modified "2023-09-27" @default.
- W25207068 title "On the Riemann-Lie algebras and Riemann-Poisson Lie groups" @default.
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