Characterizing Lie Algebra Structure via the Commutativity Degree

Puntos clave

• The research aims to identify possible values of the commutativity degree for Lie algebras and explore their structure.
• Defined the asymptotic commutativity degree of Lie algebras.
• Calculated the asymptotic commutativity degree for specific Lie algebras.
• Reviewed properties of a family of Lie algebras to demonstrate their commutativity degree.
• Established an asymptotic commutativity degree for certain Lie algebras.
• Proved the existence of Lie algebras where the asymptotic commutativity degree equals 1/q^k for all q ≥ 2 and k as a positive integer.