On the Cartan Subalgebras of Lie Algebras over Small Fields

Key Points

• This research focuses on understanding the structure and characteristics of Cartan subalgebras in Lie algebras defined over finite fields.
• Examined properties of Cartan subalgebras in Lie algebras.
• Proved the minimal dimension Lie algebra without Cartan subalgebras is semisimple.
• Analyzed specific examples within gl(n, F).
• Demonstrated that a semisimple Lie algebra can exist without Cartan subalgebras.
• Characterized Cartan subalgebras in the general linear algebraic structure gl(n, F).