臺灣博碩士論文加值系統

在Kostant的論文中，他證明了一個霍夫代數中關於單位元素的初等元素是一個有限維的子李代數，而且他也證明了這些元素所成的集合就是這個超李群在單位元素處的切平面。在這篇論文中，我們就是要找出超李群GL(m/n,R)的超李代數，並證明它與gl(m/n,R)同構。

In this paper, we study the subspace of the dual of A(G) of a Lie supergroup (G,A) where G=GL(m/n,R). We prove the Lie superalgebra of the Lie supergroup (G,A) and Lie superalgebra containing left-invariant vector fields of A(G) are both isomorphic to gl(m/n,R).

0.Introduction
1.Definitions and notations
2.Algebra and coalgebra
3.Hopf algebra structure
4.Lie superalgebra
5.The left-invariant vector fields
Referrences

[C] M.L. Curtis,Matrix Groups 2th.,Springer Verlag 1984.
[K] B.Kostant,Graded Manifolds,Graded Lie Theory,andPrequantization,Lecture Notes in Math Vol.570,pp.177-306
[Ki] A.A. Kirillov,Introduction to Superanalysis,D.Reidel Publishing Company 1978.
[M] S. Montgomery, Hopf Algebras and Their actions on Rings, AMS1993.
[W] F.W. Warner, Foundations of Differentiable Manifolds and Lie groups, Springer Verlag 1983.