Flat Nonunimodular Lorentzian Lie Algebras |
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Authors: | Mohamed Boucetta |
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Institution: | Université Cadi-Ayyad, Faculté des sciences et techniques, Marrakech, Marocco |
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Abstract: | A flat Lorentzian Lie algebra is a left symmetric algebra endowed with a symmetric bilinear form of signature (?, +,…, +) such that left multiplications are skew-symmetric. In geometrical terms, a flat Lorentzian Lie algebra is the Lie algebra of a Lie group with a left-invariant Lorentzian metric with vanishing curvature. In this article, we show that any flat nonunimodular Lorentzian Lie algebras can be obtained as a double extension of flat Riemannian Lie algebras. As an application, we give all flat nonunimodular Lorentzian Lie algebras up to dimension 4. |
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Keywords: | Double extension Flat Lorentzian Lie algebras Nonunimodular Lie algebras Representations of solvable Lie algebras |
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