Structures Of3-Lie Bialgebras

The paper mainly concerns structures of3-Lie bialgebras over a field of characteristic0. The concept of3-Lie bialgebras is provided. For a given3-Lie bialgebra (L, μ,),the structure of the dual algebra (L,, μ) is studied, and the relation between twoalgebras is discussed, where L is the dual space of L and, μ are dual mappings,respectively. It is proved that (L, μ,) is a3-Lie bialgebra if and only if the dualalgebra (L,, μ) is a3-Lie bialgebra.The paper consists of four sections. Section1introduces the back ground anddevelopment of n-Lie algebras. Section2provides some definitions and some basic resultswhich are used in the paper. Section3gives the concept of3-Lie bialgebra and studiesits structures. The last section is the summarization of the paper and gives the prospectof the study.