TOPICS IN GROUP THEORY AND LIE ALGEBRAS
| Title | ΘΕΩΡΙΑ ΟΜΑΔΩΝ ΚΑΙ LIE ΑΛΓΕΒΡΩΝ / TOPICS IN GROUP THEORY AND LIE ALGEBRAS |
| Code | Θ004 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Athanasios Papistas |
| Common | Yes |
| Status | Active |
| Course ID | 600025884 |
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 | 600268377
|
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268377
Language of Instruction
- Greek (Instruction, Examination)
Learning Outcomes
Upon successful completion of the course, the students will be in position to combine Group Theory with Lie algebras.
General Competences
- Work in an interdisciplinary team
- Generate new research ideas
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Free group Fn of finite rank n (definition, construction, properties of Fn), Free abelian group of finite rank n, Free nilpotent group of finite rank n, Nielsen-Schreier Theorem, the automorphism group of Fn, IA-automorphisms of Fn.
Lie algebras (Preliminaries, construction of free Lie algebra of finite rank, basis, subalgebras of free Lie algebra, Free associative algebra, Construction of Lie algebra via group, The Johnson Lie algebra L(IA(Fn)), Andreadakis’ conjecture.
Keywords
Free group of finite rank, (IA)-Automorphisms, Associated Lie algebra, Andreadakis;conjecture
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Seminars | 100 | ||||
| Reading Assigment | 158 | ||||
| Exams | 3 | ||||
| Total | 300 |
Student Assessment
Description
Written exam.
Student Assessment methods
- Written Exam with Problem Solving (Summative)
Bibliography
Additional bibliography for study
1. Y. Bahturin, Identical relations in Lie algebras, VNU Science Press, Utrecht, 1987.
2. N. Jacobson, Lie algebras, Dover Publications, Inc. New York, 1962.
3. D. Johnson, Presentations of groups, London Mathematical Society, Student Texts 15, Cambridge University Press 1990.
4. R.C. Lyndon and P.E. Schupp, Combinatorial Group Theory, Springer-Verlag, New York, 1977.
5. W. Magnus, A. Karrass, D. Solitar, Combinatorial Group Theory, Interscience, John Wiley and Sons, New York, 1966.
6. H. Neumann, Varieties of groups, Springer-Verlag, Berlin, 1967.
7. C. Reutenauer, Free Lie algebras, Oxford University Press Inc., New York 1993.
8. Α.Ι. Πάπιστας, Μαθήματα Θεωρίας Ομάδων, Ελληνικά Ακαδημαϊκά Ηλεκτρονικά Συγγράμματα και Βοηθήματα, ΕΜΠ, ΣΕΑΒ 2015.
Last Update
30-11-2024
