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Coursebooks 2017-2018
Lie groups
MATH-477
Lecturer(s) :
Raum SvenLanguage:
English
Summary
This course introduces to Lie groups and their correspondence with Lie algebras. Classical groups and compact groups are treated as important classes of examples. The notions of homogeneous spaces and lattices are introduced.Content
- Lie groups and their Lie algebras
- Classical groups
- Compact (Lie) groups
- Homogeneous spaces and lattices in Lie groups
Keywords
Lie groups, Lie group-Lie algebra correspondence, homogeneous spaces
Learning Prerequisites
Required courses
- Topology (MATH-225)
- Introduction aux varietés différentiables (MATH-322)
- Group theory (MATH-211)
Learning Outcomes
By the end of the course, the student must be able to:- Structure the relationship between Lie groups and Lie algebras
- Define classical groups
- Describe basic properties of classical groups
- Compute the representation theory of compact Lie groups
- Explain examples of lattices and homogeneous spaces
Transversal skills
- Continue to work through difficulties or initial failure to find optimal solutions.
- Take feedback (critique) and respond in an appropriate manner.
- Demonstrate the capacity for critical thinking
- Demonstrate a capacity for creativity.
- Make an oral presentation.
Teaching methods
Ex-cathedra course with exercises
Expected student activities
- Participate in the course
- Solve regular exercises
- Present exercises in the classroom
- Acquire one short piece of mathematics independently
Assessment methods
Oral exam and presentation in the classroom. In case Art. 3 al. 5 of the regulations of the section apply to some student, the exam form will be decided by the teacher and communicated to the student.
Supervision
Office hours | Yes |
Assistants | Yes |
Forum | No |
Resources
Bibliography
- Alexander Kirillov, Jr. An introduction to Lie groups and Lie algebras. ISBN-13: 978-0-521-88969-8
- Sigurdur Helgason. Differential geometry, Lie groups, and symmetric spaces. ISBN-13: 978-0821828489
- Sigfried Echterhoff & Anton Deitmar. Principles of harmonic analysis. ISBN-13: 978-3319057910
- Theodor Bröcker & Tammo tom Dieck. Representations of compact Lie groups. ISBN-13: 978-3540136781
- David Witte Morris. Introduction to arithmetic groups. ISBN-13: 978-0986571602
Ressources en bibliothèque
In the programs
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Lie groups - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Lie groups - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Lie groups - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Lie groups - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Lie groups - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
- SemesterSpring
- Exam formOral
- Credits
5 - Subject examined
Lie groups - Lecture
2 Hour(s) per week x 14 weeks - Exercises
2 Hour(s) per week x 14 weeks
- Semester
Reference week
Mo | Tu | We | Th | Fr | |
---|---|---|---|---|---|
8-9 | |||||
9-10 | |||||
10-11 | MAA330 | MAA110 | |||
11-12 | |||||
12-13 | |||||
13-14 | |||||
14-15 | |||||
15-16 | |||||
16-17 | |||||
17-18 | |||||
18-19 | |||||
19-20 | |||||
20-21 | |||||
21-22 |
Lecture
Exercise, TP
Project, other
legend
- Autumn semester
- Winter sessions
- Spring semester
- Summer sessions
- Lecture in French
- Lecture in English
- Lecture in German