Conformal Vector Fields on Lorentzian Lie Groups of Dimension 4

Key Points

• The central aim is to classify Lorentzian Lie groups of dimension 4 that feature non-Killing left-invariant conformal vector fields.
• Classification approach based on mathematical principles of Lie groups.
• Exploration of the properties of Lorentzian geometry and conformal mappings.
• Assessment of left-invariance in vector fields.
• Identification of specific Lorentzian Lie groups that possess non-Killing left-invariant conformal vector fields.
• Establishment of criteria for the existence of such vector fields in four-dimensional spaces.