A-扩张Lie Rinehart代数的证明及其应用

The Proof and Application of A-Expanding Lie Rinehart Algebra

本文简单介绍Lie Rinehart代数的范畴和关于一个有幺,交换,结合代数A的光滑流形的概念.我们特别指出一种叫做A-扩张代数的代数,以及作用代数都可以实现为李群上的A-左不变向量场所构成的空间.这是通常的李代数与李群关系的推广.

In this thesis,we introduce the contents of Lie Rinehart algebra and such manifolds that connect to combinatory and abelian A algebra which has and unit.Especially we point out another algebra-A expanding algebra as well as the vector space which are constitutes of A left invariant vector field.This left invariant vector field can be achieved on Lie group by algebra.This is the spread of the relationship between Lie algebra and Lie group.