Affine actions on Nilpotent Lie groups
Burde, Dietrich ; Dekimpe, Karel ; Deschamps, Sandra
arXiv, 0711.4959 / Harvested from arXiv
Text on arXiv
To any connected and simply connected nilpotent Lie group N, one can associate its group of affine transformations Aff(N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N, via such affine transformations. We succeed in translating the existence question of such a simply transitive affine action to a corresponding question on the Lie algebra level. As an example of the possible use of this translation, we then consider the case where dim(G)=dim(N) less than 6. Finally, we specialize to the case of abelian simply transitive affine actions on a given connected and simply connected nilpotent Lie group. It turns out that such a simply transitive abelian affine action on N corresponds to a particular Lie compatible bilinear product on the Lie algebra of N, which we call an LR-structure.
Publié le : 2007-11-30
Classification:  Mathematics - Differential Geometry,  Mathematics - Group Theory,  22E25,  17B30 
@article{0711.4959,
     author = {Burde, Dietrich and Dekimpe, Karel and Deschamps, Sandra},
     title = {Affine actions on Nilpotent Lie groups},
     journal = {arXiv},
     volume = {2007},
     number = {0},
     year = {2007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0711.4959}
}

Burde, Dietrich; Dekimpe, Karel; Deschamps, Sandra. Affine actions on Nilpotent Lie groups. arXiv, Tome 2007 (2007) no. 0, . http://gdmltest.u-ga.fr/item/0711.4959/