Geodesic
On the Cartan Subalgebras of Lie Algebras over Small Fields
Salvatore Siciliano1, 2, 3, 4, 5
1Dip. di Matematica, Università di Lecce, 73100 Lecce, Italy
2We study Cartan subalgebras of Lie algebras defined over finite fields. We prove that a possible Lie algebra of minimal dimension without Cartan subalgebras is semisimple. Subsequently, we study Cartan subalgebras of gl(n, F).
3Keywords: Lie algebras, Cartan subalgebras, finite fields.
4MSC: 17B50
5[
Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 511-518

Voir la notice de l'article provenant de la source Heldermann Verlag

We study Cartan subalgebras of Lie algebras defined over finite fields. We prove that a possible Lie algebra of minimal dimension without Cartan subalgebras is semisimple. Subsequently, we study Cartan subalgebras of gl(n, F).
Classification : 17B50
Mots-clés : Lie algebras, Cartan subalgebras, finite fields

Salvatore Siciliano  1 , 2 , 3 , 4 , 5

1 Dip. di Matematica, Università di Lecce, 73100 Lecce, Italy
2 We study Cartan subalgebras of Lie algebras defined over finite fields. We prove that a possible Lie algebra of minimal dimension without Cartan subalgebras is semisimple. Subsequently, we study Cartan subalgebras of gl(n, F).
3 Keywords: Lie algebras, Cartan subalgebras, finite fields.
4 MSC: 17B50
5 [ 
Salvatore Siciliano. On the Cartan Subalgebras of Lie Algebras over Small Fields. Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 511-518. http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a11/
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     author = {Salvatore Siciliano},
     title = {On the {Cartan} {Subalgebras} of {Lie} {Algebras} over {Small} {Fields}},
     journal = {Journal of Lie Theory},
     pages = {511--518},
     year = {2003},
     volume = {13},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a11/}
}
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