Frontiers of Mathematics in China >

2010 , Vol. 5 >Issue 1: 103 - 115

DOI: https://doi.org/10.1007/s11464-009-0055-z

Research articles

Leibniz algebras with pseudo-Riemannian bilinear forms

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  • 1.Sino-European Institute of Aviation Engineering, Civil Aviation University of China, Tianjin 300300, China; 2.School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;

Published date: 05 Mar 2010

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Abstract

M. Bordemann has studied non-associative algebras with nondegenerate associative bilinear forms. In this paper, we focus on pseudo-Riemannian bilinear forms and study pseudo-Riemannian Leibniz algebras, i.e., Leibniz algebras with pseudo-Riemannian non-degenerate symmetric bilinear forms. We give the notion and some properties of T∗-extensions of Leibniz algebras. In addition, we introduce the definition of equivalence and isometrical equivalence for two T∗-extensions of a Leibniz algebra, and give a sufficient and necessary condition for the equivalence and isometrical equivalence.

Key words： Leibniz algebra; T∗-extension; pseudo-Riemannian bilinear form

Cite this article

Jie LIN, Zhiqi CHEN, . Leibniz algebras with pseudo-Riemannian bilinear forms[J]. Frontiers of Mathematics in China, 2010 , 5(1) : 103 -115 . DOI: 10.1007/s11464-009-0055-z

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