2018 Advanced topics in Geometry G

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Honda Nobuhiro 
Course component(s)
Lecture     
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.

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