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

Abstract

In this paper, the ternary differential system with nonlinearities of degree six is investigated. For this system, nine Lie operators providing a linear representation of one-parameter elementary groups are determined in the space of phase variables and coefficients. The commutators of these operators, which form a Lie algebra L₉, are constructed. The structure constants are determined, and the type of the Lie algebra is analyzed. By means of the Killing form, it is proved that the Lie algebra L₉ is reductive.