
Journal of Lie Theory 32 (2022), No. 2, 383412 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 torsionfree 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 torsionfree 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 nonvanishing l^{q,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. [ Fulltextpdf (212 KB)] for subscribers only. 