Compatibility Conditions on the Reduced Poisson-Lie Group

被引：0

作者：

Aloui, Foued ^{[1
]}

Zaalani, Nadhem ^{[2
]}

机构：

[1] Higher Sch Sci & Technol Hammam Sousse, St Lamine Abassi,BP 4011, Hammam Sousse, Tunisia

[2] Higher Inst Appl Sci & Technol, Sousse St Tahar Ben Achour,BP 4003, Sousse, Tunisia

来源：

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS | 2020年 / 44卷 / 02期

关键词：

Poisson Geometry; Riemannian Geometry; Lie group and Lie algebra;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (G, Lambda(G), <,>(G)) be a Poisson Lie-group equipped with a left invariant Riemannian metric and H a normal and closed coisotropic subgroup of G. In this paper, we give necessary and sufficient conditions so that the compatibility conditions between the Poisson tensor A G and the metric <,>(G) on G remain verified on the reduced Poisson-Lie group (G/H, Lambda(G/H), <,>(G/H)). In particular, if the immersed dual group (G/H)* is totally geodesic in G* then, these conditions are satisfied.

引用

页码：149 / 166

页数：18

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