Left-invariant Lorentzian Flat Metrics on Lie Groups

Key Points

• 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.

Abstract