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.
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, Tome 22 (2012) no. 1, pp. 269-289. http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a10/
@article{JOLT_2012_22_1_a10,
author = {Malika Ait Ben Haddou and Mohamed Boucetta and Hicham Lebzioui},
title = {Left-invariant {Lorentzian} {Flat} {Metrics} on {Lie} {Groups}},
journal = {Journal of Lie Theory},
pages = {269--289},
year = {2012},
volume = {22},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a10/}
}
TY - JOUR
AU - Malika Ait Ben Haddou
AU - Mohamed Boucetta
AU - Hicham Lebzioui
TI - Left-invariant Lorentzian Flat Metrics on Lie Groups
JO - Journal of Lie Theory
PY - 2012
SP - 269
EP - 289
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a10/
ID - JOLT_2012_22_1_a10
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%0 Journal Article
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%A Mohamed Boucetta
%A Hicham Lebzioui
%T Left-invariant Lorentzian Flat Metrics on Lie Groups
%J Journal of Lie Theory
%D 2012
%P 269-289
%V 22
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a10/
%F JOLT_2012_22_1_a10
