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401-3222-00L 8 Credits BSC , DR , MSC D-USYS , D-MAVT , D-MTEC , D-MATH , D-BIOL , D-PHYS , D-CHAB

Introduction to Lie Groups

Lecturers & Examiners: Prof. em. Dr. Alessandra Iozzi
VVZ CR n/a

Last Updated: 2026-02-05 15:19:32

Abstract

1) Definition, basic properties. Lie subgroups.2) Lie algebras and their relation with Lie groups: exponential map, adjoint representation.3) Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's theorem, Engel's theorem.4) Definition of algebraic groups and relation with Lie groups.5) Applications: Lie groups in the diffeomorphism group of a manifold, invariant volume.

Resources

Literature

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)

General Information

Language
English
Levels
BSC , DR , MSC

Examination

Type
session examination
Mode
oral 20 minutes

Course Components

Type Title Time & Place Hours
lecture Introduction to Lie Groups
  • Tue 13:15-14:00 (HG E 1.1)
  • Thu 13:15-15:00 (HG E 1.1)
  • 23.03 Date 10:15-12:00 (HG F 26.3)
3 h weekly
exercise Introduction to Lie Groups
  • Tue 12:15-13:00 (HG E 1.1)
  • Thu 13:15-15:00 (HG D 5.3)
  • Thu 13:15-15:00 (HG F 26.3)
1 h weekly

Offered In