Affine actions on Nilpotent Lie groups
| dc.creator | Burde, Dietrich | |
| dc.creator | Dekimpe, Karel | |
| dc.creator | Deschamps, Sandra | |
| dc.date | 2007-11-30 | |
| dc.date.accessioned | 2026-07-07T08:46:27Z | |
| dc.date.available | 2026-07-07T08:46:27Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0711.4959 | |
| dc.identifier | http://arxiv.org/abs/0711.4959 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143253 | |
| dc.subject | Differential Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 22E25; 17B30 | |
| dc.title | Affine actions on Nilpotent Lie groups | |
| dc.type | text |