GROUPS AND LIES ALGEBRAS
| Title | ΟΜΑΔΕΣ ΚΑΙ ΑΛΓΕΒΡΕΣ LIE / GROUPS AND LIES ALGEBRAS |
| Code | Θ031 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Panagiotis Batakidis |
| Common | Yes |
| Status | Active |
| Course ID | 600025920 |
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 | 600268392
|
Type Of Offer
- Disciplinary Course
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268392
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Knowledge of differential manifolds is required. Basic knowledge of group theory, integration on manifolds and general topology is desirable.
Learning Outcomes
- they will know the basic definitions of the theory of Lie algebras and their most important families.
- they will know the construction of a Lie group from a Lie algebra, and the corresponding geometric interpretations with examples.
- they will understand the basic results of Lie group theory and the related analysis
- they will know the initial steps for the construction and study of representations of Lie groups
General Competences
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Adapt to new situations
- Make decisions
- Work autonomously
- Work in teams
- Generate new research ideas
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Groups and Lie Algebras. Lie algebras and exponential mapping. Linear differential operators and one-parameter groups. Differentials and automorphisms. Subgroups and Lie subalgebras. Quotient. Fundamental Lie Theorems. Simply coherent Lie groups. Solvable and nullable Lie groups. Compact Lie groups: Tori. Compact Lie algebras. Compact form and Haar measure. Semisimple Lie groups: Cartan and Iwasawa decompositions. Integration.
Keywords
Lie Theory, Integration, Analysis on Lie groups, Representation Theory of Lie groups
Educational Material Types
- Notes
- Slide presentations
- Multimedia
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
- Use of ICT in Student Assessment
Description
Online exercise hours
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Reading Assigment | 183 | ||||
| Tutorial | 13 | ||||
| Project | 20 | ||||
| Written assigments | 40 | ||||
| Exams | 5 | ||||
| Total | 300 |
Student Assessment
Description
There will be assignments due by the end of the semester (30% of the final grade), together with a small project (40%) and an oral exam or midterm (30%)
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
- Performance / Staging (Formative, Summative)
Bibliography
Additional bibliography for study
-Lie Groups, Lie Algebras and Representations, B.C. Hall, Springer, GTM 222, Second Edition, 2015
-Lie Groups, C. Procesi, Springer, Universitext, 2007
-Structure and Geometry of Lie Groups, J. Hilgert & K.-H. Neeb, Springer, Monographs in Mathematics, 2012
-Differential Geometry and Mathematical Physics, G. Rudolph & M. Schmidt, Springer, Theoretical and Mathematical Physics, 2013
Last Update
12-05-2025
