MATH513 REPRESENTATION THEORY OF FINITE GROUPS
| Course Code: | 2360513 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. SEMRA ÖZTÜRK |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will learn:
- basic concepts used in representation theory, such as modules, in particular modules over group algebras over fields, decomposing modules into irreducibles via indecomposables in the algebra
- differences between modules over semisimple versus non-semisimple algebras, and characterictic zero versus characteristic p>0 fields
- computing character tables,
- obtaining information about the group from the character table of the group
- restriction to a subgroup and inducing from a subgroup of representations
Course Content
Ring theoretic preliminaries. Group representations and their characters. Characters, integrality and application to the structure theory of finite groups. Product of characters. Induced characters. Reduction and extension of characters. Brauer's theorem on characterization of characters.
Course Learning Outcomes
Introduction to modules and algebras. In particular modules/representations of group algebras kG, and their characters. The cases of the characteristic 0 and a prime p for the field k will be learned in detail. Products and induction and restriction of characters/modules will be learned.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution