Pseudo-Riemannian Lie groups admitting left-invariant conformal vector fields

Abstract

Let $G$ be a Lorentzian Lie group or a pseudo-Riemannian Lie group of type $(n-2,2)$. If $G$ admits a non-Killing left-invariant conformal vector field, then $G$ is solvable.

Keywords

• Conformal vector fields
• Killing vector fields
• Pseudo-Riemannian Lie groups
• Lorenztian Lie groups