Gradings for nilpotent Lie algebras. (English) Zbl 1498.17047
Summary: 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.
MSC:
| 17B70 | Graded Lie (super)algebras |
| 22E25 | Nilpotent and solvable Lie groups |
| 17B40 | Automorphisms, derivations, other operators for Lie algebras and super algebras |
| 20F65 | Geometric group theory |
| 20G20 | Linear algebraic groups over the reals, the complexes, the quaternions |
Keywords:
nilpotent Lie algebras; gradings; maximal gradings; positive gradings; stratifications; Carnot groups; classifications; large scale geometry; Heintze groups; lqp cohomologyReferences:
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