Journal of Lie Theory

no. 1
Left-invariant Lorentzian Flat Metrics on Lie Groups
Malika Ait Ben Haddou1; Mohamed Boucetta2; Hicham Lebzioui1
1Faculté des Sciences, Meknes, Morocco
2Université Cadi-Ayyad, Faculté des Sciences Gueliz, Marrakech, Morocco
Journal of Lie Theory, Volume 22 (2012) no. 1, pp. 269-289
We call the Lie algebra of a Lie group with a left invariant pseudo-Riemannian flat metric pseudo-Riemannian flat Lie algebra. We give a new proof of a classical result of Milnor on Riemannian flat Lie algebras. We reduce the study of Lorentzian flat Lie algebras to those with trivial center or those with degenerate center. We show that the double extension process can be used to construct all Lorentzian flat Lie algebras with degenerate center generalizing a result of Aubert-Medina on Lorentzian flat nilpotent Lie algebras. Finally, we give the list of Lorentzian flat Lie algebras with degenerate center up to dimension 6.
DOI: 10.5802/jolt.669
Classification: 53C50, 16T25, 53C20, 17B62
Keywords: Coadjoint orbit, integral coadjoint orbit

Malika Ait Ben Haddou  1 ; Mohamed Boucetta  2 ; Hicham Lebzioui  1

1 Faculté des Sciences, Meknes, Morocco
2 Université Cadi-Ayyad, Faculté des Sciences Gueliz, Marrakech, Morocco 
Malika Ait Ben Haddou; Mohamed Boucetta; Hicham Lebzioui. Left-invariant Lorentzian Flat Metrics on Lie Groups. Journal of Lie Theory, Volume 22 (2012) no. 1, pp. 269-289. doi: 10.5802/jolt.669
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     title = {Left-invariant {Lorentzian} {Flat} {Metrics} on {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {269--289},
     year = {2012},
     volume = {22},
     number = {1},
     doi = {10.5802/jolt.669},
     zbl = {1243.53110},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.669/}
}
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