In this program
- Finite groups
- Lie groups and Lie algebras
- Advanced topics
Lie groups and Lie algebras
Representation theory · Theoretical / proof-based
Lie groups: examples and exponential map
Objectives
- Lie groups: examples and exponential map
- Lie algebras
- Semisimplicity
- Representations of sl(2, C)
- Weight spaces
- Root systems and Weyl group (introduction)
- Highest weight theory for semisimple Lie algebras (overview)
Study materials
- Study guideComing soon
- Exam StrategyComing soon
- Common MistakesComing soon
- WorksheetsComing soon
- Word problemsComing soon
- Mixed PracticeComing soon
- Multi-Unit ProblemsComing soon
- ReviewComing soon
- Practice testComing soon
- Answer keyComing soon
Interactive practice
Quizzes, typed answers, and flashcards for this unit — coming soon.
- Coming soon
Quiz
Multiple-choice questions with instant feedback
- Coming soon
Typed practice
Type answers and check them
- Coming soon
Flashcards
Vocabulary and key facts
- Coming soon
Mixed quiz
Harder mixed review for this standard