Gradings for nilpotent Lie algebras
Group Theory
2022-01-14 v3 Differential Geometry
Metric Geometry
Rings and Algebras
Abstract
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 cohomology.
Cite
@article{arxiv.2011.06871,
title = {Gradings for nilpotent Lie algebras},
author = {Eero Hakavuori and Ville Kivioja and Terhi Moisala and Francesca Tripaldi},
journal= {arXiv preprint arXiv:2011.06871},
year = {2022}
}
Comments
35 pages, minor presentation improvements