2020/11/13 by Hakavuori, Eero, Kivioja, Ville, Moisala, Terhi +1
#17B40 #17B70 (Primary) #20F65 #20G20 (Secondary) #22E25 #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2011.06871
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.