Fundamental concepts in Lie groups and Lie algebra will be explained, including many basic examples. This course will be succeeded by MTH.B504
To understand basic properties of Lie groups and Lie algebra
To be familiar with basic examples of Lie groups and Lie algebra
To be familiar with homogeneous spaces
Lie group, Lie algebra, exponential map, local isomorphism, homogeneous space
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
standard lecture course
Course schedule | Required learning | |
---|---|---|
Class 1 | definition of Lie group, homomorphism | Details will be provided during each class session |
Class 2 | definition of Lie algebra, relation between Lie group and Lie algebra | |
Class 3 | exponential mapping | |
Class 4 | local isomorphism | |
Class 5 | universal covering group | |
Class 6 | homogeneous space and examples | |
Class 7 | linear representation of Lie group |
none
Warner, "Foundation of differential manifolds and Lie groups" GTM 94, Chapter 3
homework
No prerequisites.