§ 歷史背景

Sophus Lie   Wilhelm Killing   Elie Cartan   Hermann Weyl

[簡介與習作]

[from SO(2) to SO(3)]  [證明O(n)是李群]      [李群與微分方程]      [Iwasawa分解定理]      [Hyperbolic Plane]

§ 物理上的應用

1. 何謂E8李群 ? [A Garrett Lisi]李斯
2. 規範場論

1. Lie group理論中 李氏積關鍵性的決定了群的無窮小結構(infinitesimal structure of the group)  大域微分幾何 p.112
2. 積分因子--李群之觀點   林琦焜
3. Sophus Lie's Approach to Differential Equations (S.Helgason)
4. [群表現(Representation)] (數學傳播季刊 36卷第4期)
5. [Elie Cartan的故事]
6. S^0,S^1,S^3 are the only spheres which are also groups(Lie groups)

1. [Introduction to Lie Groups and Lie Algebras]   Alxander Kirillov Jr.
2. [Foundations of Differentiable Manifolds and Lie Groups] Frank W.Warner
3. [Lectures on Lie Groups] 項武義
4. Lie Groups for Pendestrians---on line
5. [Lie algebras for physicists] Douglas W.Mckenzie
6. [Lie Groups New Research]   Altos B. Canterra
   關於Clifford algebra 1990年 David Hestenes(1933~ ) [Space-Time algebra]認識到Clifford algebra及其在量子力學的解釋(電子自旋)
   1965年 Harry J. Lipkin(1921~ ) 在[Lie group for Pendestrains]中引用Clifford algebra
   [Lie group Guide to the Universe]是Altos B. Canterra寫的一本小冊子 解釋李代數在Clifford代數中的意義
7. [Lie Groups,Differential Equations and geometry] Giovanni Falcone