MAT 261, Spring 2022


Instructor: Eugene Gorsky, egorskiy AT
Office hours: Thursdays 3-4pm on zoom.
If you have a question and cannot come at office hours, write me an email to schedule an appointment.


The textbook for the course is "Lie Groups, Lie Algebras, and Representations" by Brian C. Hall.

Final grade

The grade will be 100% based on the homeworks, the lowest homework score is dropped. There will be no midterms or final exam.


1. Lie groups, examples. Topological properties. Homomorphisms. (Hall, section 1)
HW 1 , HW 2
Lectures 1, 2, 3, 4, 5

2. Exponential map, one-parameter subgroups. Closed subgroup theorem (w/o proof). (Hall, section 2)
HW 3
Lectures 6, 7, 8

3. Lie algebras: definition, basic properties, homomorphisms. Simple, solvable and nilpotent Lie algebras. Lie algebras for matrix Lie groups. (Hall, section 3).
HW 4
Lectures 9, 10, 11, 12, 13

4. Representation theory of sl(2,C) (Hall, section 4.6)
HW 5 , HW 6
Lectures 14, 15, 16, 17

5. Semisimple Lie algebras. Roots, Cartan subalgebras, Weyl group. Killing form (Hall, section 7).
Lectures 18, 19, 20, 21, 22, 23

6.Representations of semisimple Lie algebras: weights, Verma modules, finite-dimensional representations (Hall, section 9).
Lectures 24,25, 26.

Disability Services

Any student with a documented disability who needs to arrange reasonable accommodations must contact the Student Disability Center (SDC). Faculty are authorized to provide only the accommodations requested by the SDC. If you have any questions, please contact the SDC at (530)752-3184 or