The Lie algebra admitted by the ternary differential system with nonlinearities of degree six

Key Points

• Examine the Lie algebra associated with a ternary differential system that features nonlinearities of degree six.
• Identified nine Lie operators within the phase variables and coefficients.
• Constructed commutators from the identified operators to form the Lie algebra L₉.
• Determined structure constants and analyzed the Lie algebra's type.
• Used the Killing form to investigate the properties of the Lie algebra.
• Established that the Lie algebra L₉ is reductive.
• Characterized the structure of the Lie algebra through its commutators.
• Provided insights into the implications of the Killing form for the algebra's classification.