Geodesic
Filiform Lie Algebras Without Rational Structures
Journal of Lie theory, Tome 26 (2016) no. 4, pp. 991-1
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Hamrouni and Souissi gave a sufficient condition for a family of 7-dimensional filiform Lie algebras to have no rational structures and constructed an example of a 7-dimensional filiform Lie algebra without rational structures explicitly. In this paper, we give a sufficient condition for arbitrary-dimensional filiform Lie algebras to have no rational structures. Moreover, we consider a sufficient condition for products of filiform Lie algebras and arbitrary nilpotent Lie algebras to have no rational structures and give infinitely many new examples of nilpotent Lie algebras without rational structures.
Classification : 22E40
Mots-clés : Nilpotent Lie algebras, filiform Lie algebras, rational structures 
@article{JLT_2016_26_4_JLT_2016_26_4_a2,
     author = {N. Kato},
     title = {Filiform {Lie} {Algebras} {Without} {Rational} {Structures}},
     journal = {Journal of Lie theory},
     pages = {991--1},
     year = {2016},
     volume = {26},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2016_26_4_JLT_2016_26_4_a2/}
}
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N. Kato. Filiform Lie Algebras Without Rational Structures. Journal of Lie theory, Tome 26 (2016) no. 4, pp. 991-1. http://geodesic.mathdoc.fr/item/JLT_2016_26_4_JLT_2016_26_4_a2/