MTK728 - INTRODUCTION TO REPRESENTATION THEORY of ALG. II
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| INTRODUCTION TO REPRESENTATION THEORY of ALG. II | MTK728 | 2nd Semester | 3 | 0 | 3 | 12 |
| Prequisites | none | |||||
| Course language | Turkish | |||||
| Course type | Elective | |||||
| Mode of Delivery | Face-to-Face | |||||
| Learning and teaching strategies | Lecture Discussion Question and Answer Other: Assignment | |||||
| Instructor (s) | Assoc. Prof. Dr. Bülent Saraç | |||||
| Course objective | The aim of this course is to help students interpret and apply the fundamental concepts and results given in the Representation Theory of associative algebras. | |||||
| Learning outcomes |
| |||||
| Course Content | Nakayama algebras and representation-finite group representations Tilting theory Representation-finite hereditary algebras Tilted algebras | |||||
| References | 1) Assem, D. Simson, A. Skowroski, Elements of the representation theory of associative algebras. Vol. 1. Techniques of representation theory. London Mathematical Society Student Texts, 65. Cambridge University Press, Cambridge, 2006. 2) M. Barot, Introduction to the representation theory of algebras. Springer, Cham, 2015. 3) M. Auslander, I. Reiten, S. O. Smalø, Representation theory of Artin algebras. Cambridge Studies in Advanced Mathematics, 36. Cambridge University Press, Cambridge, 1995. | |||||
Course outline weekly
| Weeks | Topics |
|---|---|
| Week 1 | The Loewy series and the Loewy length of a module , uniserial modules and right serial algebras, Nakayama algebras |
| Week 2 | Nakayama algebras, Almost split sequences for Nakayama algebras, representation?finite group algebras |
| Week 3 | Torsion pairs, tilting modules |
| Week 4 | The tilting theorem of Brenner and Butler, consequences of the tilting theorem |
| Week 5 | Separating and splitting tilting modules, torsion pairs induced by tilting modules |
| Week 6 | Midterm exam |
| Week 7 | Hereditary algebras, the Dynkin and Euclidean graphs |
| Week 8 | Integral quadratic forms, the quadratic form of a quiver |
| Week 9 | Reflection functors and Gabriel?s theorem |
| Week 10 | Gabriel?s theorem |
| Week 11 | Midterm exam |
| Week 12 | Sections in translation quivers, representation?infinite hereditary algebras |
| Week 13 | Tilted algebras, projectives and injectives in the connecting component |
| Week 14 | The criterion of Liu and Skowronski |
| Week 15 | Preparation for final exam |
| Week 16 | Final Exam |
Assesment methods
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 5 | 25 |
| Presentation | 0 | 0 |
| Project | 0 | 0 |
| Seminar | 0 | 0 |
| Midterms | 2 | 25 |
| Final exam | 1 | 50 |
| Total | 100 | |
| Percentage of semester activities contributing grade succes | 7 | 50 |
| Percentage of final exam contributing grade succes | 1 | 50 |
| Total | 100 | |
WORKLOAD AND ECTS CALCULATION
| Activities | Number | Duration (hour) | Total Work Load |
|---|---|---|---|
| Course Duration (x14) | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, ect) | 14 | 15 | 210 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 5 | 14 | 70 |
| Midterms (Study duration) | 2 | 12 | 24 |
| Final Exam (Study duration) | 1 | 14 | 14 |
| Total Workload | 36 | 58 | 360 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition level* | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| 1. Deepens the concepts of mathematics in the level of expertise. | X | ||||
| 2. Grasps the inter-disciplinary interaction related to the area; reaches original results by using the specialist knowledge in analyzing and evaluating new ideas. | |||||
| 3. Gains the ability to think independently and develops theoretical concepts. | X | ||||
| 4. Develops original mathematical models by using interrelations between mathematics and other disciplines and applies them to other disciplines. | |||||
| 5. Uses high level research methods in studies in the area. | X | ||||
| 6. Develops a new idea, method and/or application independently, finds a solution, and contributes to the progress in the area by carrying out original studies. | |||||
| 7. Fulfills the leader role in the environments where solutions are thought for the area and/or inter-disciplinary problems. | |||||
| 8. Develops continually the skills of creativity, decision making and problem solving. | X | ||||
| 9. Defends original opinions by communicating with experts in the area. | X | ||||
| 10. Uses a foreign language- at least C1 Level-, communicates with foreign colleagues and follows the international literature. | |||||
| 11. Follows the latest developments in the information and communication technologies and uses them in the area. | |||||
| 12. Does research in national and international research groups. | |||||
| 13. Makes strategic decision in the solution of problems in the area. | |||||
| 14. Protects the rights of other researchers in regards to ethics, privacy, ownership and copyright. | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest