Calculus of Variations and Geometric Measure Theory

E. Hakavuori - V. Kivioja - T. Moisala - F. Tripaldi

Gradings for nilpotent Lie algebras

created by hakavuori on 16 Nov 2020
modified by tripaldi on 02 Jan 2023


Accepted Paper

Inserted: 16 nov 2020
Last Updated: 2 jan 2023

Journal: Journal of Lie Theory
Volume: 32
Number: 2
Pages: 383--412
Year: 2022

ArXiv: 2011.06871 PDF


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 $\ell^{q,p}$ cohomology.

Tags: GeoMeG