Geodesic
Gradings on Lie algebras with applications to infra-nilmanifolds
Jonas Deré1
1KU Leuven Kulak, Kortrijk, Belgium
Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 105-120

Voir la notice de l'article provenant de la source EMS Press

DOI

In this paper, we study positive as well as non-negative and non-trivial gradings on finite dimensional Lie algebras. The existence of such a grading on a Lie algebra is invariant under taking field extensions, a result very recently obtained by Y. Cornulier and we give a different proof of this fact. Similarly, we prove that given a grading of one of these types and a finite group of automorphisms, there always exist a grading of the same type which is preserved by this group. From these results we conclude that the existence of an expanding map or a non-trivial self-cover on an infra-nilmanifold depends only on the covering Lie group. Another application is the construction of a nilmanifold admitting an Anosov diffeomorphism but no non-trivial self-covers and in particular no expanding maps, which is the first known example of this type.
DOI : 10.4171/ggd/390
Classification : 17-XX, 20-XX, 22-XX, 37-XX
Mots-clés : Infra-nilmanifolds, nilpotent Lie algebras, expanding maps, Anosov diffeomorphisms

Jonas Deré  1

1 KU Leuven Kulak, Kortrijk, Belgium 
Jonas Deré. Gradings on Lie algebras with applications to infra-nilmanifolds. Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 105-120. doi: 10.4171/ggd/390
@article{10_4171_ggd_390,
     author = {Jonas Der\'e},
     title = {Gradings on {Lie} algebras with applications to infra-nilmanifolds},
     journal = {Groups, geometry, and dynamics},
     pages = {105--120},
     year = {2017},
     volume = {11},
     number = {1},
     doi = {10.4171/ggd/390},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/390/}
}
TY  - JOUR
AU  - Jonas Deré
TI  - Gradings on Lie algebras with applications to infra-nilmanifolds
JO  - Groups, geometry, and dynamics
PY  - 2017
SP  - 105
EP  - 120
VL  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/390/
DO  - 10.4171/ggd/390
ID  - 10_4171_ggd_390
ER  - 
%0 Journal Article
%A Jonas Deré
%T Gradings on Lie algebras with applications to infra-nilmanifolds
%J Groups, geometry, and dynamics
%D 2017
%P 105-120
%V 11
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/390/
%R 10.4171/ggd/390
%F 10_4171_ggd_390

Cité par Sources :