On Riemann-Poisson Lie groups

IF 0.5 Q3 MATHEMATICS

Archivum Mathematicum Pub Date : 2019-08-14 DOI:10.5817/am2020-4-225

B. Alioune, M. Boucetta, Ahmed Sid’Ahmed Lessiad

引用次数: 2

Abstract

A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in C.R. Acad. Sci. Paris s\'er. {\bf I 333} (2001) 763-768. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.

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关于黎曼-泊松李群

黎曼-泊松李群是具有左不变黎曼度规和左不变泊松张量的李群，它们在C.R.中引入的意义上是相容的。巴黎\ ' er。{\bf I 333}(2001) 763-768。我们研究了这些李群，并给出了它们的李代数的一个表征。我们也给出了一种构造这些李代数的方法，并给出了5维李代数的列表。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archivum Mathematicum MATHEMATICS-

CiteScore

0.70

自引率

16.70%

发文量

审稿时长

35 weeks

期刊介绍： Archivum Mathematicum is a mathematical journal which publishes exclusively scientific mathematical papers. The journal, founded in 1965, is published by the Department of Mathematics and Statistics of the Faculty of Science of Masaryk University. A review of each published paper appears in Mathematical Reviews and also in Zentralblatt für Mathematik. The journal is indexed by Scopus.