Flat affine or projective geometries on Lie groups

JOURNAL OF ALGEBRA

卷:455

Article

Medina, A.^1,2  Saldarriaga, O.³  Giraldo, H.³ 

[1] Univ Montpellier, Inst A Grothendieck, CNRS, UMR 5149, Montpellier, France

[2] Univ Antioquia, Antioquia, Colombia

[3] Univ Antioquia, Inst Matemat, Antioquia, Colombia

关键词: Flat affine Lie groups;    Flat projective Lie groups;    Affine transformations;    Projective transformations;    Projective etale representations;   

DOI  :  10.1016/j.jalgebra.2016.02.007

来源: Elsevier

【 摘 要 】

This paper deals essentially with affine or projective transformations of Lie groups endowed with a flat left invariant affine or projective structure. These groups are called fiat alpine or fiat projective Lie groups. We give necessary and sufficient conditions for the existence of fiat left invariant projective structures on Lie groups. We also determine Lie groups admitting flat bi-invariant affine or projective structures. These groups could play an essential role in the study of homogeneous spaces M = G/H having a flat affine or fiat projective structures invariant under the natural action of G on M. A. Medina asked several years ago if the group of affine transformations of a flat affine Lie group is a flat projective Lie group. In this work we provide a partial positive answer to this question. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free