Classification On Low Dimensional Lie Super Bialgebras

In this paper, we try to discuss the classification of low dimensional Lie super algebras. This paper is divided into three parts: In the first section, we introduce some basic definitions and results. The definition of Lie algebra and Lie coalgebra and Lie bialgebra as well as the classification of Lie algebras, whose dimension is lower than or equal to 3. In the section, we review the definition of Lie super algebra. And we give the definition of Lie super coalgebra and Lie super bialgebra. More over, we discuss the classification of low dimensional Lie super algebra. In the section, we classify the Lie super bialgebras, whose dimension is lower than or equal to 3.