Capability of Low-Dimensional Nilpotent 3-Lie Algebras

Key Points

• This research aims to investigate the capability of nilpotent n-Lie algebras based on their dimensions and characteristics.
• Characterization of nilpotent n-Lie algebras of dimension at most n + 3 over arbitrary fields.
• Analysis of 7-dimensional nilpotent 3-Lie algebras over fields with characteristic not equal to 2.
• Characterized capability for nilpotent n-Lie algebras when n > 2 particularly regarding dimension constraints.
• Specifically examined properties of 7-dimensional nilpotent 3-Lie algebras and their dependence on field characteristics.