Algebra II (ΑΛ2)
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General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | ΑΛ2 |
| Semester | 2 |
| Course Title | Algebra II |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | General Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students | Yes (in English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The main purpose of the course is to introduce the student to the basic concepts, results, tools and methods of the Representation Theory of Finite Groups and its applications to other areas of Mathematics, mainly in Group Theory, and other related sciences, e.g. in Physics. At the end of the course, we expect the student to understand the basic concepts and the main theorems that are analysed in the course, to understand how these are applied to concrete examples arising from different thematic areas of Mathematics and related sciences, to be able to apply them to derive new elementary consequences in various fields, and finally to be able to perform some (not so obvious) calculations related to several problems arising in Group Theory. |
|---|---|
| General Competences |
The course aims at enabling the graduate student to acquire the ability to analyse and synthesize basic knowledge of the basic Representation Theory of Finite Groups, which is an important part of modern Mathematics with numerous applications to other sciences, for instance in Physics. When the graduate student comes in for the first time in connection with the basic notions of representation theory and its applications to group theory, (s)he strengthens her/his creative, analytical and inductive thinking, and her/his ability to apply abstract knowledge in different areas of central interest in Mathematics and related sciences. |
Syllabus
- Representations and characters of groups.
- Groups and homomorphisms.
- FG-modules και group-algebras.
- Schur’s Lemma and Maschke’s Theorem.
- Group-algebras and irreducible modules.
- Conjugacy classes and characters.
- Character tables and orthogonality relations.
- Normal subgroups and lifted characters.
- Elementary examples of characters tables.
- Tensor products. Restricting representations to subgroups.
- Applications.
Teaching and Learning Methods - Evaluation
| Delivery |
Face to face | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
The evaluation is based on the combined performance of the graduate student in:
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Attached Bibliography
- J.P. Serre: “Linear Representations of Finite Groups”, Springer-Verlag, (1977).
- B. Steinberg: “Representation Theory of Finite Groups: An Introductory Approach”, Springer, (2012).
- C.W. Curtis and V. Reiner: “Methods of Representation Theory: With Applications to Finite Groups and Orders”, Wiley, (1981).
- P. Etingof et al: “Introduction to Representation Theory”, Student Mathematical Library 59, AMS, (2011).
- J.L. Alperin and R.B. Bell: “Groups and Representations”, Springer (1995).
- M. Burrow: “Representation Theory of Finite Groups”, Academic Press, (1965).
- M. Liebeck and G. James: “Representations and Characters of Groups”, CUP, (2001).