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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On pseudo-Riemannian Lie algebras


Authors: Zhiqi Chen, Mingming Ren and Fuhai Zhu
Journal: Proc. Amer. Math. Soc. 138 (2010), 2677-2685
MSC (2010): Primary 17B60, 17D25
Published electronically: April 2, 2010
MathSciNet review: 2644884
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Abstract: In this paper, we show that $ {\mathfrak{g}} {\mathfrak{g}}\subset{\mathfrak{g}}$ if $ {\mathfrak{g}}$ is a pseudo-Riemannian Lie algebra with $ C(\mathfrak{g})\not=0$. Then we show that $ {\mathfrak{g}}{\mathfrak{g}}\subset{\mathfrak{g}}$ when $ \dim\mathfrak{g}=4$, which leads to the classification of the pseudo-Riemannian Lie algebras in dimension 4.


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Additional Information

Zhiqi Chen
Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Email: chenzhiqi@nankai.edu.cn

Mingming Ren
Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Email: rmingming@gmail.com

Fuhai Zhu
Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Email: zhufuhai@nankai.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10325-6
PII: S 0002-9939(10)10325-6
Keywords: Pseudo-Riemannian Lie algebra, solvable Lie algebra
Received by editor(s): October 8, 2009
Received by editor(s) in revised form: November 6, 2009, November 16, 2009, and November 25, 2009
Published electronically: April 2, 2010
Additional Notes: The third author is the corresponding author. He was supported in part by NNSF Grant #10971103.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.