On pseudo-Riemannian Lie algebras
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- by Zhiqi Chen, Mingming Ren and Fuhai Zhu
- Proc. Amer. Math. Soc. 138 (2010), 2677-2685
- DOI: https://doi.org/10.1090/S0002-9939-10-10325-6
- Published electronically: April 2, 2010
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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.References
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Bibliographic 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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2677-2685
- MSC (2010): Primary 17B60, 17D25
- DOI: https://doi.org/10.1090/S0002-9939-10-10325-6
- MathSciNet review: 2644884