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This research aims to explore the characteristics of Lorentzian flat Lie algebras, particularly those with degenerate centers.

March 29, 2026Journal of Lie theoryOpen Access

Left-invariant Lorentzian Flat Metrics on Lie Groups

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This research aims to explore the characteristics of Lorentzian flat Lie algebras, particularly those with degenerate centers.
Provided a new proof for Milnor's classical result on Riemannian flat Lie algebras.
Reduced the study of Lorentzian flat Lie algebras to those with trivial or degenerate centers.
Utilized the double extension process to construct all Lorentzian flat Lie algebras with degenerate centers.
Compiled a list of Lorentzian flat Lie algebras with degenerate centers up to dimension 6.
Verified the classical results on the structures of flat Lie algebras.
Established a comprehensive framework for analyzing Lorentzian flat Lie algebras.
Generated a complete list of such algebras up to dimension 6.

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New proofs reveal structures of Lorentzian flat Lie algebras, indicating a path for further exploration.

Haddou et al. (2012) studied this question.

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