Low dimensional Lie groups admitting left invariant flat projective or affine structures

Abstract

We prove that any real Lie group of dimension \leq 5 admits a left invariant flat projective structure. We also prove that a real Lie group L of dimension \leq 5 admits a left invariant flat affine structure if and only if the Lie algebra of L is not perfect.

16 pages

References in corpus (1)

• Left-symmetric algebras, or pre-Lie algebras in geometry and physics

Cited by in corpus (1)

• Projectively flat and affinely flat parabolic subgroups of special linear groups