We present a constructive approach to torsion-free gradings of Lie algebras. Our main result is the computation of a maximal grading. Given a Lie algebra, using its maximal grading we enumerate all of its torsion-free gradings as well as its positive gradings. As applications, we classify gradings in low dimension, we consider the enumeration of Heintze groups, and we give methods to find bounds for non-vanishing lq,p cohomology.
Eero Hakavuori
1
;
Ville Kivioja
2
;
Terhi Moisala
2
;
Francesca Tripaldi
3
1
SISSA, Trieste, Italy
2
Faculty of Mathematics and Science, University of Jyväskylä, Finland
3
Faculty of Science, University of Bern, Switzerland
Eero Hakavuori; Ville Kivioja; Terhi Moisala; Francesca Tripaldi. Gradings for Nilpotent Lie Algebras. Journal of Lie Theory, Tome 32 (2022) no. 2, pp. 383-412. http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a3/
@article{JOLT_2022_32_2_a3,
author = {Eero Hakavuori and Ville Kivioja and Terhi Moisala and Francesca Tripaldi},
title = {Gradings for {Nilpotent} {Lie} {Algebras}},
journal = {Journal of Lie Theory},
pages = {383--412},
year = {2022},
volume = {32},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a3/}
}
TY - JOUR
AU - Eero Hakavuori
AU - Ville Kivioja
AU - Terhi Moisala
AU - Francesca Tripaldi
TI - Gradings for Nilpotent Lie Algebras
JO - Journal of Lie Theory
PY - 2022
SP - 383
EP - 412
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a3/
ID - JOLT_2022_32_2_a3
ER -
%0 Journal Article
%A Eero Hakavuori
%A Ville Kivioja
%A Terhi Moisala
%A Francesca Tripaldi
%T Gradings for Nilpotent Lie Algebras
%J Journal of Lie Theory
%D 2022
%P 383-412
%V 32
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a3/
%F JOLT_2022_32_2_a3
