Post Lie Super Algebra Structure On A (0,1)

Lie superalgebras and Lie algebras act an important role in mathematical physics, and it makes the study of Lie superalgebras and related topics become one of the most active ?elds in mathematics. In the past ten years, the research of Lie superalgebras has experienced a series of development. Especially, in the struction and the representation of simple Lie superalgebras. Because the even part of Lie superalgebra is a lie algebra, the methods to research Lie superalgebras are often copied from the methods of Lie algebra.The concept of Post Lie algebra was introduced by Vallette while he studied the cohomology and Koszul operator in 2007.So far,the research of Post Lie algebra has a certain achievement.For example,it has been given that the complete classi?cation of Post Lie algebra structure on the Lie algebra sl(2, C) and gl(2, C).In the ?rst chapter,it introduces the backgroud of the research and the trend of this passage.It also suggests the struction of this passage.Then in the second chapter,it introduces the concept of Lie superalgebra, Post Lie superalgebra and the isomorphism of Lie superalgebra.It also introdues three algebras,gl(2, C),A1 and A(0,1).Finally in the third chapter,it introduces some theories and the struction of Post Lie superalgebra on A(0,1).