Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 13, No. 2, pp. 511--518 (2003)

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On the Cartan Subalgebras of Lie Algebras over Small Fields

Salvatore Siciliano

Salvatore Siciliano
Dip. di Matematica E. De Giorgi
Università degli Studi di Lecce
Via Provinciale Lecce-Arnesano
73100-LECCE, Italy
salvatore.siciliano@unile.it

Abstract: In this note 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 $\frak{gl}(n,F)$.

Keywords: Lie algebras, Cartan subalgebras, finite fields

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Electronic version published on: 26 May 2003. This page was last modified: 14 Aug 2003.

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