REPRESENTATION THEORY OF GROUPS AND ALGEBRAS
| Title | ΑΝΑΠΑΡΑΣΤΑΣΕΙΣ ΟΜΑΔΩΝ ΚΑΙ ΑΛΓΕΒΡΩΝ / REPRESENTATION THEORY OF GROUPS AND ALGEBRAS |
| Code | Θ001 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Chrysostomos Psaroudakis |
| Common | No |
| Status | Active |
| Course ID | 600025881 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268374
|
Type Of Offer
- Disciplinary Course
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268374
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
Learning Outcomes
The students will be able to
1. understand techniques of representation theory with various applications
2. compute representations of groups
3. compute representations of algebras
4. compute representations of modules via quivers
5. realise the interpretation of finite representation type of an algebraic structure
General Competences
- Work autonomously
- Work in teams
- Generate new research ideas
Course Content (Syllabus)
The course is an introduction to representation theory of groups and algebras. Algebras. Algebras. Modules and Representations. Simple Modules and Jordan-Hölder Theorem. Semisimple Modules and Semisimple Algebras. Artin-Wedderburn Theorem. Groupalgebras and Maschke's Theorem. Indecomposable Modules. Representation Type. Representations of Quivers. Gabriel's Theorem. Almost Split Sequences. Auslander-Reiten Quiver of an Algebra. Algebras of Finite Representation Type.
Keywords
Groups. Algebras. Modules. Semisimple Modules. Artin-Wedderburn Theorem. Group Algebras. Indecomposable Modules. Quivers. Gabriel's Theorem. Algebras of Finite Representation Type.
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Seminars | 58 | ||||
| Reading Assigment | 200 | ||||
| Exams | 3 | ||||
| Total | 300 |
Student Assessment
Description
The grading will be obtained in three parts:
(i) Exercise sheets through all semester, percentage of the final degree 20%.
(ii) First written exam in the first half of the course, percentage of the final degree 20%.
(iii) Second written exam in the other half of the course, percentage of the final degree 30%.
The final grade is the overall sum of the above intermediate exams.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative)
- Written Exam with Extended Answer Questions (Formative)
- Written Assignment (Formative)
- Oral Exams (Formative)
- Written Exam with Problem Solving (Formative)
Bibliography
Additional bibliography for study
1) Assem, F. Coelho, "Basic Representation Theory of Algebras".
2) K. Erdmann, T. Holm, "Algebras and Representation Theory".
3) M. Auslander, I. Reiten, O. Smalo, "Representation Theory of Artin Algebras".
4) I.Assem, A.Skowronski, D.Simson, "Elements of the Representation Theory of Associative Algebras".
Last Update
01-12-2024
