Journal of Lie Theory

no. 4
Filiform Lie Algebras Without Rational Structures
Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 991-1000
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.
DOI: 10.5802/jolt.920
Classification: 22E40
Keywords: Nilpotent Lie algebras, filiform Lie algebras, rational structures 
@article{JOLT_2016_26_4_a2,
     author = {N. Kato},
     title = {Filiform {Lie} {Algebras} {Without} {Rational} {Structures}},
     journal = {Journal of Lie Theory},
     pages = {991--1000},
     year = {2016},
     volume = {26},
     number = {4},
     doi = {10.5802/jolt.920},
     zbl = {1404.17022},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.920/}
}
TY  - JOUR
AU  - N. Kato
TI  - Filiform Lie Algebras Without Rational Structures
JO  - Journal of Lie Theory
PY  - 2016
SP  - 991
EP  - 1000
VL  - 26
IS  - 4
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.920/
DO  - 10.5802/jolt.920
ID  - JOLT_2016_26_4_a2
ER  - 
%0 Journal Article
%A N. Kato
%T Filiform Lie Algebras Without Rational Structures
%J Journal of Lie Theory
%D 2016
%P 991-1000
%V 26
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.920/
%R 10.5802/jolt.920
%F JOLT_2016_26_4_a2
N. Kato. Filiform Lie Algebras Without Rational Structures. Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 991-1000. doi: 10.5802/jolt.920

Cited by Sources: