MATH615 LIE ALGEBRAS
| Course Code: | 2360615 |
| 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: | Prof.Dr. ÖMER KÜÇÜKSAKALLI |
| Offered Semester: | Fall Semesters. |
Course Objectives
Lie groups and Lie algebras are especially important in the study of group actions on vector spaces. Besides explaining problems in several areas in mathematics, Lie algebras are interesting in their own right. The classification of simple complex Lie algebras is a beautiful application of linear algebra. The aim of this course is to introduce some of the techniques for studying Lie algebras.
Course Content
Basic Concepts, semisimple Lie Algebras, root systems, isomorphism and conjugacy theorems, existence theorem.
Course Learning Outcomes
Upon completion of this course, the student will
- understand the classification of semisimple complex Lie algebras,
- be able to analyze the representations associated with certain algebras,
- be able to recognize certain symmetries, namely the elements of the Weyl group, that can be used in different branches of mathematics.
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