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- School of Science
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School of Engineering
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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Honda Nobuhiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri5-6(H103)
- Group
- -
- Course number
- MTH.B503
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 3Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
Fundamental concepts in Lie groups and Lie algebra will be explained, including many basic examples. This course will be succeeded by MTH.B504
Student learning outcomes
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
Keywords
Lie group, Lie algebra, exponential map, local isomorphism, homogeneous space
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
standard lecture course
Course schedule/Required learning
| 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 |
Textbook(s)
none
Reference books, course materials, etc.
Warner, "Foundation of differential manifolds and Lie groups" GTM 94, Chapter 3
Assessment criteria and methods
homework
Related courses
- MTH.B504 ： Advanced topics in Geometry H
Prerequisites (i.e., required knowledge, skills, courses, etc.)
No prerequisites.
