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

2014/06/13 by Hironao Kato, Kato, Hironao
Mathematics · #53A15 #53A20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1406.3424

openalex publication_date 2014/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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