臺灣博碩士論文加值系統

令V為一n 維的向量空間，且附有一個非退化的對稱雙線形式。令G為V上保持此雙線形式的線性函數所組成的群。此論文探討G及其軌道的拓樸性質，以及G的李代數。

Let V be an n-dimensional vector space, equipped with a non-degenerate symmetic bilinear form. Let G be the group of all linear mappings on V which preserves this bilinear form. In this thesis, we study the topological properties of G and its orbits, as well as the Lie algebra of G.

1. Introduction
2. Inner product
3. Orthogonal and unitary groups
4. Topological properties of groups
5. Topological properties of orbits
6. Real forms of complex Lie algebras
7. The Lie algebra su(p,q)

{1} J.e.Humphreys, Introduction to Lie algebra and Representation Thery, Springer, 1972.
{2} Morton L.Curtis, Matrix Groups, Second Ediction, Springer.