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Journal of Lie Theory 13 (2003), No. 2, 511--518
Copyright Heldermann Verlag 2003

On the Cartan Subalgebras of Lie Algebras over Small Fields

Salvatore Siciliano
Dip. di Matematica, UniversitÓ di Lecce, 73100 Lecce, Italy

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).

Keywords: Lie algebras, Cartan subalgebras, finite fields.

MSC: 17B50

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