On pseudo-Riemannian Lie algebras: a class of new Lie-admissible algebras

2008/07/07 by Chen, Zhiqi, Fuhai Zhu, Zhu, Fuhai
Mathematics · #17D25 #Advanced Topics in Algebra #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0807.0936

openalex publication_date 2008/07/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

M. Boucetta introduced the notion of pseudo-Riemannian Lie algebra in [2] when he studied the line Poisson structure on the dual of a Lie algebra. In this paper, we redefine pseudo-Riemannian Lie algebra, which, in essence, is a class of new Lie admissible algebras and prove that all pseudo-Riemannian Lie algebras are solvable. Using our main result and method, we prove some of M. Boucetta's results in [2, 3] in a simple and new way, then we give an explicit construction of Riemann-Lie algebras and a classification of pseudo-Riemannian Lie algebras of dimension 2 and 3.

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