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| 研究生： |
施如怡 Shih, Ju-yi |
|---|---|
| 論文名稱： |
有限維單李代數的建造 Construction of finite dimensional simple Lie algebras from root systems |
| 指導教授： |
林牛
Ngau Lam |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系應用數學碩博士班 Department of Mathematics |
| 論文出版年： | 2008 |
| 畢業學年度： | 96 |
| 語文別： | 英文 |
| 論文頁數： | 17 |
| 外文關鍵詞： | Non-simply-laced Lie algebras, Simply-laced Lie algebras, Root system |
| 相關次數： | 點閱：63 下載：3 |
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In this thesis, we will review the construction of finite dimensional simple Lie algebras through root systems.
First, we construct the simply-laced Lie algebras of types An,Dn,E6,E7 and E8 by using their root lattices and a bi-multiplicative map. We then construct the non-simply-laced Lie algebras of types Bn,Cn,F4 and G2 using an automorphism of order 2 or 3 of the Lie algebras of types An,Dn and E6.
R. W. Carter, Lie Algebras of Finite and Affine Type,
Cambridge University Press, Cambridge, 2005.
K. Erdmann, M. J. Wildon, Introduction to Lie algebras, Springer, London, 2006.
I. Frenkel, J. Lepowsky, A. Meurman, Vertex Operator
Algebras and The Monster, Academic Press, Boston, 1988.
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, 1972.
V. Kac, Infinite-Dimensional Lie Algebras, Third edition, Cambridge University Press, Cambridge, 1990.
D. Mitzman, Integral Bases for Affine Lie Algebras and Their Universal Enveloping Algebras, Providence, RI., American Mathematical Society, 1985.
校內：2009-07-30公開校外：2009-07-30公開