On pseudo-Euclidean Lie algebras whose Levi-Civita product is left Leibniz

被引：2

作者：

Benayadi, Said ^{[1
]}

Boucetta, Mohamed ^{[2
]}

机构：

[1] Univ Lorraine, Lab IECL, CNRS UMR 7502, UFR MIM, 3 Rue Augustin Frenel,BP 45112, F-57073 Metz 03, France

[2] Univ Cadi Ayyad, Fac Sci & Tech, BP 549, Marrakech, Morocco

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2023年 / 87卷

关键词：

Leibniz algebra; Pointed Lie rack; Left invariant pseudo-Riemannian; metric on Lie groups; Levi-Civita product; Flat pseudo-Euclidean Lie algebras; Quadratic Lie algebras; Milnor Lie algebras; Double extension; NILPOTENT; METRICS;

D O I：

10.1016/j.difgeo.2023.101986

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a class of Lie algebras which contains the class of quadratic Lie algebras and the class of Milnor Lie algebras, namely, Lie algebras endowed a pseudo -Euclidean metric such its Levi-Civita product is left Leibniz. We call them Levi-Civita left Leibniz Lie algebras LCLL for short. We show that a Lie group (G, h) endowed with a left invariant pseudo-Riemannian such that the corresponding Lie algebra is LCLL is complete and locally symmetric. Moreover, there is a pointed Lie rack structure on G whose corresponding left Leibniz algebra is given by the Levi-Civita product. Euclidean LCLL Lie algebras are the product of a quadratic Lie algebra and a flat Euclidean Lie algebra. We develop an adapted version of the process of double extension to construct LCLL Lie algebras. We show that Lorentzian or flat LCLL Lie algebras can be obtained by this process.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：25

共 20 条

[1] On nilpotent and simple Leibniz algebras [J].