# Reading Group - Fall 2021

### Finite and Infinite Dimensional Lie Algebra Representation

# Welcome to our Reading Group

We are planning to read the textbook Introduction to Finite and Infinite Dimensional Lie (Super)algebras throughout this semester. Our ambitious plan is to finish chapter 1 on finite dimensional Lie Algebra and reaching the basic of Kac-Moody algebra. The reading group will be held weekly and we will take turn present what we learned from the textbook. We will also try to do some exercises from this old class at MIT instructed by Victor Kac

# Day 1: Saturday September 4th

## Announcements and Agendas:

- Organizational Meeting

# Day 2: Saturday September 11th

## Announcements and Agendas:

- Subalgebras of Lie algebras.
- 4 families of classical Lie algebras: \(A_n, B_n, C_n, D_n\) and their bases
- Lie algebra representation definition, adjoint representation
- Engel's theorem

# Day 3: Saturday September 25th

## Announcements and Agendas:

- Lie's Theorem
- Lie's Lemma

# Day 4: Saturday October 2nd

## Announcements and Agendas:

- Generalized weighted space and eigenspace
- Zariski topology and regular element

# Day 5: Saturday October 9th

## Announcements and Agendas:

- Cartan subalgebra

# Day 6: Saturday October 16th

## Announcements and Agendas:

- Killing form