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

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

2008-07-07

arxiv.org/abs/0807.0936v1

Mathematics

Rings and Algebras

10 pages

Scientific paper

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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