# Group Theory (1394-1395)

- Prerequisites:
- I follow my own lecture notes which you can download form this page. However as we go along, I may upgrade these lecture notes and post the revised note on this page. So you may want to wait until I possible revise each lecture note and then download the new ones. A list of other helpful references may be:
- Group theory, by Joshi
- Lie algebras in particle physics, Howard Georgi
- Group theory for physicists, by Wybourne
- Weekly schedule:
- Groups, matrix groups, permutation and braid groups, generators and relations.
- structures within a group, subgroups, classes, cosets, factor groups, centers of a group, normalizers.
- Homomorphism, Isomorphism, the fundamental theorem of Isomorphisms.
- Action of a group on a manifold,
- The general linear Matrix group and its subgroups.
- Topological groups.
- Manifolds and their tangent spaces, Lie groups and their Lie algebras,
- Representation theory of finite groups,
- The structure of Lie Algebras, subalgebras, ideals, homomorphisms, solvable and nilpotent algebras, Killing form, simple and semi-simple algebras,
- The structure of semi-simple Lie algebras, roots, simple roots, positive roots, Cartan basis, Dynkin diagrams,
- Classification of simple Lie algebras and its proof.
- Representation of Lie algebras.

Linear algebra is an essential prerequisite of this course. Quantum mechanics I is also extermely useful.

Saturday and Monday: 2:00 to 4:00 Pm

# Contents

# Lecture Notes

- Lecture Notes