Conformal Vector Fields on Lie Groups of Dimension 4 with Signature of (2,2)

Key Points

• The aim is to classify 4-dimensional Lie groups that have a (2,2) signature and support non-Killing left-invariant conformal vector fields.
• Classification approach for Lie groups
• Analysis of conformal vector field properties
• Investigation of left-invariant fields
• Identified specific classes of 4-dimensional Lie groups
• Characterized the structure of conformal vector fields
• Demonstrated the existence of non-Killing fields in these Lie groups