Gradings for Nilpotent Lie Algebras
Copyright policy )Gradings for Nilpotent Lie Algebras
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.
35 pages, minor presentation improvements
- University of Bern Switzerland
maximal gradings, Mathematics - Differential Geometry, Heintze groups, nilpotent Lie algebras, classifications, Group Theory (math.GR), Mathematics - Metric Geometry, FOS: Mathematics, gradings, Nilpotent and solvable Lie groups, Automorphisms, derivations, other operators for Lie algebras and super algebras, Metric Geometry (math.MG), Mathematics - Rings and Algebras, positive gradings, 17B70 (Primary), 22E25, 17B40, 20F65, 20G20 (Secondary), Differential Geometry (math.DG), Carnot groups, large scale geometry, Rings and Algebras (math.RA), Graded Lie (super)algebras, Linear algebraic groups over the reals, the complexes, the quaternions, stratifications, Geometric group theory, Mathematics - Group Theory, lqp cohomology
maximal gradings, Mathematics - Differential Geometry, Heintze groups, nilpotent Lie algebras, classifications, Group Theory (math.GR), Mathematics - Metric Geometry, FOS: Mathematics, gradings, Nilpotent and solvable Lie groups, Automorphisms, derivations, other operators for Lie algebras and super algebras, Metric Geometry (math.MG), Mathematics - Rings and Algebras, positive gradings, 17B70 (Primary), 22E25, 17B40, 20F65, 20G20 (Secondary), Differential Geometry (math.DG), Carnot groups, large scale geometry, Rings and Algebras (math.RA), Graded Lie (super)algebras, Linear algebraic groups over the reals, the complexes, the quaternions, stratifications, Geometric group theory, Mathematics - Group Theory, lqp cohomology
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