Lie Groups and Lie Algebras Mini-course
李群与李代数短课
Notice
Lecture videos are available on our bilibili channel.
Speakers
- Li, Yining(李亿宁)
- Lin, Wangyang(林汪炀)
- Liu, Zhilin(刘祉麟)
- Tan, Tianrui(谭田瑞)
- Wang, Xinrui(王心睿)
- Wu, Tong(吴桐)
- Wu, Zongsheng(邬宗圣)
- Zhang, Xiping(张希平)
Schedule
Lectures
- 2023/7/24
- Wu, Zongsheng
- Basic Definitions and Examples about Lie Algebras
- Notes
- 2023/7/26
- Wu, Zongsheng
- Engel Theorem, Lie Theorem and Jordan-Chevalley Decomposition
- Notes Part 1
- Notes Part 2
- 2023/8/2,2023/8/4
- Liu, Zhilin
- Smooth Manifolds, and Topological Groups
- TBD
- Liu, Zhilin and Tan, Tianrui
- Definitions and Examples about Lie Groups, Lie Derivatives and the Exponential Maps
- TBD
- Wang, Xinrui
- Covering Maps of Lie Groups
- TBD
- Lin, Wangyang
- The de Rham Theory of Lie Groups
- All the notes will be published when all my talks are finished.
- TBD
- Lin, Wangyang
- Cohomology of Lie Algebras I: Introduction
- TBD
- Lin, Wangyang
- Cohomology of Lie Algebras II: Whitehead Lemmas and Weyl Theorem
- TBD
- Zhang, Xiping
- Cartan Subalgebras and the Root Systems
- TBD
- Zhang, Xiping
- Finite-Dimensional Representations of $\mathfrak{sl}(2)$
- TBD
- Wu, Tong
- Weyl Groups
- TBD
- Wu, Tong
- The Fundamental dominant weight and the highest weight
Bonus
- TBD
- Wang, Xinrui
- Classification of Admissible Representations of $GL(2,\mathbb{R})$
- TBD
- Li, Yining
- Coxeter Groups
References
- Introduction to Lie Algebras and Representation Theory, by J.E. Humphreys
- Lie Groups Beyond an Introduction, by Anthony W. Knapp
- Lie Groups, Lie Algebras and Representations: An Elementary Introduction, by Brian Hall