Introduction to Lie Groups Autumn 2019

Paul D. Nelson
Subhajit Jana

We will try to linearly follow the book OV. The tentative topics are 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.


Topology, multivariable calculus, 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.

Course Notes

  • This is Lie Group course note taught by Prof. Nelson in Autumn 2016.
  • There will be exercise classes, approximately bi-weekly, replacing lecture hours. Our plan is to solve all the exercises in the first chapter of the text book OV.

    The next exercise class will be on 31st October. We wil do problems 9-16 in the page 39 of OV.

    LectureTuesday 10:00-12:00HG D 3.2
    LectureThursday 08:00-10:00HG D 3.2