Geodesic
Gradings for Nilpotent Lie Algebras
Journal of Lie theory, Tome 32 (2022) no. 2, pp. 383-412
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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.
Classification : 17B70, 22E25, 17B40, 20F65, 20G20
Mots-clés : Nilpotent Lie algebras, gradings, maximal gradings, positive gradings, stratifications, Carnot groups, classifications, large scale geometry, Heintze groups, lqp cohomology 
@article{JLT_2022_32_2_JLT_2022_32_2_a3,
     author = {E. Hakavuori and V. Kivioja and T. Moisala and F. Tripaldi},
     title = {Gradings for {Nilpotent} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {383--412},
     year = {2022},
     volume = {32},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2022_32_2_JLT_2022_32_2_a3/}
}
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E. Hakavuori; V. Kivioja; T. Moisala; F. Tripaldi. Gradings for Nilpotent Lie Algebras. Journal of Lie theory, Tome 32 (2022) no. 2, pp. 383-412. http://geodesic.mathdoc.fr/item/JLT_2022_32_2_JLT_2022_32_2_a3/