# Group Theory

- 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:
- Teaching Assistant:
- 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.

Sunday and Tuesday: 3:00 to 4:30 Pm

Not yet fixed

# Contents

# Lecture Notes

- Lecture Notes

# Homeworks

- Homeworks:
Set no. 1 Set no. 2 Set no. 3 Set no. 4 Set no. 5 Set no. 6 Set no. 7 Set no. 8 Set no. 9

# Grading system (New)

- Grading system:
- All the students are divided into groups consisting of at most three members each.
- The students are expected to form their favorite groups in the first week of the semester. The first set of exercises which are delivered automatically fixes the membership of groups. Absolutely no changes will be accepted later on.
- Each Monday a set of homework will be assigned and posted in this webpage.
- Every set should be solved and returned to me on the due dates. Absolutely no delay will be accepted.
- The exercises are to be solved on a cooperative basis by the members of each group. By cooperative basis we mean that any every single problem should be discussed and worked out by the collaboration of all the members of the group.
- Only one of the exercises in each set will be picked up randomly and graded.
- The grades are announced on a weekly basis on the homepage of the course.
- According to your grade in the final exams, the percentage of your homework grades will be calculated from the following table. The homework sets will be assigned every week which you should return the solutions in due time. You are supposed to work out the homework exercises in collaboration with the members of your group. Each group should consist of no more than 3 students.
- Important Note:

% of Homework grade in final grade |
% of final exam in the final grade |
The interval of final grade |

30 |
70 |
0-10 |

50 |
50 |
10-12 |

60 |
40 |
12-14 |

80 |
20 |
14-20 |

In grading the homework, I have also a look at your activity in the class. Therefore two members of the same group may be given two different grades for their homework.