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Introduction to Lie Groups
Last Updated: 2026-02-05 16:37:27
Abstract
Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups.
Objective
The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it.
Resources
Literature
A. Knapp: "Lie groups beyond an Introduction" (Birkhaeuser) A. Sagle & R. Walde: "Introduction to Lie groups and Lie algebras" (Academic Press, '73) F. Warner: "Foundations of differentiable manifolds and Lie groups" (Springer) H. Samelson: "Notes on Lie algebras" (Springer, '90) S. Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, '78) A. Knapp: "Lie groups, Lie algebras and cohomology" (Princeton University Press)
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- DR
- Frequency
- Yearly recurring
Examination
- Type
- ungraded semester performance
Registration & Places
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise |
Introduction to Lie Groups
Groups are selected in myStudies.
|
|
4 h weekly |
Offered In
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Doctorate Mathematics (More Information at: )
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Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
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Graduate School (Official website of the Zurich Graduate School in Mathematics: )
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