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

Authors
  • Chen, Zhiqi
  • Zhu, Fuhai
Type
Preprint
Publication Date
Jul 06, 2008
Submission Date
Jul 06, 2008
Source
arXiv
License
Yellow
External links

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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