# Groups and Symmetries

## General information

The course is taught by professor Van Proeyen. Contrary to the name of the course, the course is not so much about (Lie) groups, bust mostly about Lie algebra's. During the semester, about five take home assignments have to be completed. They make up four points of the exam. Van Proeyen is very generous with points on these assignments. The final exam is partially closed book, partially open book.

## Exam questions

### 2020-2021

### 2019-2020

The final exam in January 2020 consisted of two parts, each worth 8 points - their difficulty is indeed comparable. The first part is a written exam of the "open book" type, hence one is allowed to use all course material whilst solving this part. The other part of the exam consists of an oral examination, for which no auxiliary materials are allowed. The written part of the january exam in 2019-2020 contained a (rather lengthy but straightforward) question to calculate the structure constants of a matrix Lie algebra, and a question on working with Young tableaux (a third question, was of a more theoretical nature). For the oral part, there is no preparation time: one student after another goes to prof. Van Proeyen, he asks you about 8 short questions, you can think about each question a few seconds and then have to answer it. This may sound uncomfortable, but the questions are almost all about things that you should know by heart, such as definitions (e.g. group, Lie bracket), standard examples (matrix algebras, the 6 finite root systems that can be drawn in two dimensions) and constructions (distinguishing positive and negative roots, simple roots and the Cartan matrix). For some questions somewhat more insight is required, but overall this part is certainly not meant to be impossible.

### 2018-2019

Note that this year, the evaluation was different.