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Gradings for nilpotent Lie algebras
Eero Hakavuori, Ville Kivioja, Terhi Moisala, Francesca Tripaldi
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Contents
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Front Matter
Acknowledgements
1
Introduction
Overview
Implemented algorithms and applications
Structure of the paper
2
Preliminaries
On base fields
Gradings and equivalences
Universal realizations
Gradings induced by tori
Maximal gradings
3
Constructions
Enumeration of torsion-free gradings
Stratifications
Positive gradings
Maximal gradings
4
Applications
Structure from maximal gradings
Classification of gradings in low dimension
Enumerating Heintze groups
Bounds for non-vanishing \(\ell^{q,p}\) cohomology
Back Matter
A
Complete classification in low dimension
Overview
Dimension 2
Dimension 3
Dimension 4
Dimension 5
Dimension 6
Dimension 7
B
Notation
References
Authored in PreTeXt
Dimension 3
L3_1
3.3
a
(1, 0, 0)
(0, 1, 0)
(0, 0, 1)
<Y_3>
<Y_2>
<Y_1>
2.11
a
(1, 0)
(0, 1)
<Y_1, Y_2>
<Y_3>
1.001
a
1
<Y_1, Y_2, Y_3>
L3_2
[Y_1, Y_2]
=
Y_3
2.3
a
(1, 0)
(0, 1)
(1, 1)
<Y_1>
<Y_2>
<Y_3>
1.11
a
1
0
<Y_2, Y_3>
<Y_1>
b
1
2
<Y_1, Y_2>
<Y_3>
0.001
a
0
<Y_1, Y_2, Y_3>