有关A-李群及相关算子的讨论.pdf

℄ A- A- ℄ A- A- Poisson A-  A- 1. A- 2. A- ℄ A- A- ℄ A- A-  A- ℄ F ∗ iX iY LX LY Poisson C− Poisson ℄ : A- A- A- Poisson II ℄ Abstract A-manifold is a natural generalization of the concept of manifold. Then A-lie group can also be regarded as the natural generalization of the concept of lie group. But just as we know, they also have many character- istics of bundles and algebra. In this paper, we did some researches on its basic properties in terms of A-lie group by introducing the concept of both A-lie group metahomomorphism and complex poisson affine group.And we hope to deepen our comprehension of A-lie group. This paper was divided into the following two parts: Part 1. Discussion on A-lie group; Part 2. Discussion on two special kinds of A-manifold. In the section 1.1, we mainly research the intersection of A-lie groups and the product of A-lie groups, ect. By defining A-lie group metahomo- morphism we discuss some properties about A-lie group metahomomor- phism, and then we get some good conclusions in the section 1.2. In the Part 2 two special kinds of A-manifolds are discussed. In the section 2.1, ∗ the relations among pull-back operator F , retraction operator iX ,iY and lie derivative L ,L are given. By studying the concept of complex poisson X Y affine group its sufficient and necessary condition is given in last section. Key words: smooth A- structure, A-Lie group, A-Lie group meta- III