(O)-operators on a type of 4-dimensional 3-Lie algebra and 3-Pre-Lie algebras
The Operad theory of Lie algebras was applied to 3-Lie algebras,leading to the construction of 3-Pre-Lie algebras,which shared many similar properties with Pre-Lie algebras.The cubic nonlinear equations were studied by using Maple software based on the classification of 4-dimensional complex 3-Lie algebras and their relationship with structure constants of (O)-operators.The (O)-operators associated with adjoint representa-tions on a type of 4-dimensional complex 3-Lie algebras were investigated.In addition,based on the obtained results,26 examples of 3-Pre-Lie algebras derived from these (O)-operators were presented.
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