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MATH4405 Lie Groups and Lie Algebras |
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Number of Credits |
3 |
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Teaching Hours |
48 |
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Offering School |
School of Mathematical Sciences |
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Course Teacher |
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Course Level |
Undergraduate Level |
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Language of Instruction |
English |
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First Day of Class |
Monday, February17th, 2025 |
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Last Day of Class |
Monday, June 2nd, 2025 |
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Course Component |
Lecture/Discussion |
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Mode of Teaching |
Synchronous |
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Meeting Time |
Week 1-16: Mondays, 08:00-10:45 PM |
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Time Zone |
Beijing Time（UTC+8） |
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Course-specific Restrictions (e.g. Prerequisites / Major / Year of Study) |
Advanced undergraduate mathematical analysis |
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Course Description |
The purpose of this course is to provide an introduction to Lie groups and Lie algebras. This course is divided into two parts taught every Spring semester. The first part presents the basic structure theory of complex semi-simple Lie algebras up to and including the classification by Dynkin diagrams. The second part presents the basic theory of Lie groups starting with elementary properties and going through the standard results up to and including Lie’s Third Theorem.
For the first part, a good knowledge of advanced linear algebra is needed. For the second part, familiarity with manifolds is advised but not necessary since it will be reviewed. The two parts are independent of each other. The basic reference books are Humphries “Introduction to Lie algebras and their representations”, Duistermaat and Kolk “Lie Groups”, Knapp “Lie groups, beyond an introduction”, plus other secondary sources that could serve for additional reading, depending on the tine interests of the students. Depending on the background and interest of the students, the material of the course can emphasize certain topics.
Lie theory is basic to most areas of mathematics, physics, and engineering. The goal is to familiarize the students with this theory so that they can use Lie theory in their own course work and research. In this class, Professor could answer students’ questions in 6 languages: English, German, French, Spanish, Portuguese, Romanian. |
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Syllabus |
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Assessment Format |
100% Final Report |
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This course is available on APRU-VSE platform. |
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