Journal of Lie Theory 32 (2022), No. 2, 383--412
Copyright Heldermann Verlag 2022
Gradings for Nilpotent Lie Algebras
Eero Hakavuori
SISSA, Trieste, Italy
eero.hakavuori@sissa.it
Ville Kivioja
Faculty of Mathematics and Science, University of Jyväskylä, Finland
kivioja.ville@gmail.com
Terhi Moisala
Faculty of Mathematics and Science, University of Jyväskylä, Finland
moisala.terhi@gmail.com
Francesca Tripaldi
Faculty of Science, University of Bern, Switzerland
francesca.tripaldi@math.unibe.ch
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.
Keywords: Nilpotent Lie algebras, gradings, maximal gradings, positive gradings, stratifications, Carnot groups, classifications, large scale geometry, Heintze groups, lqp cohomology.
MSC: 17B70, 22E25, 17B40, 20F65, 20G20.
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