Introduction to Lie Groups Autumn 2021

Alessandra Iozzi
Lisa Ricci


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.


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.


Topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester.


Exercise sessions take place on Thursdays every second week in HG E 1.2 from 10-12. The first exercise session will be on the 30th of September.

The lecture will start on Wednesday, 22nd of September 2021 and takes place every week on

  • Wed. 8-10 in ML E 12, and
  • Th. 10-12 in LFO C 13

  • Lectures will be in-person. According to the ETH Guidelines a Covid Certificate together with an ID card or Legi should be presented to enter the room for in-person teaching.
    It is possible to follow the lecture live on Zoom. The recurring Zoom meetings for the lectures can be found here. The lecture is recorded and the recordings and lecture notes will be uploaded on this page.

    Every second week on Thursday there will be an exercise session (instead of the lecture). The first exercise session is on Thursday 30th September.