Topological Matrix Groups (MAE826)
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General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAE826 |
| Semester |
8 |
| Course Title |
Topological Matrix Groups |
| Independent Teaching Activities |
Interactive, Presentations (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background, skills development |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek, English |
| Is the Course Offered to Erasmus Students |
Yes |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The aim of the course is to provide an introduction to Lie theory through matrix groups. The main subject of study is the closed subgroups of the general linear group. Our study is extended from real to complex and quaternion numbers. The corresponding linear groups are in fact topological groups and an introduction of basic properties of topological group is also provided. The Lie algebra of a matrix group is defined. The special orthogonal, unitary and symplectic groups provide important example of Lie algebras. Lie algebras are studied using the exponential map. Finally Lie groups are defined. |
|---|---|
| General Competences |
|
Syllabus
- General linear groups
- Real and Complex algebras, Quaternions. Matrix algebras
- Inner product, orthogonal, unitary and symplectic groups
- Homomorphisms
- Differential curves, tangent vectors. Dimension of a matrix group
- Differential homomorphisms
- Expontential and logarithmic funcions. Lie algebras
- Special orthogonal and symplectic groups
- Topological groups, manifolds
- Maximal tori
- Differential manifolds, Lie groups.
Teaching and Learning Methods - Evaluation
| Delivery |
Face-to-face, Distance learning | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology |
Communication with students | ||||||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
Written Examination, Oral Presentation, written assignments. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- J. F. Adams, Lectures on Lie groups, University of Chicago Press, 1969.
- M. L. Curtis, Matrix Groups, Springer-Verlag, 1979.
- R. Howe. Very basic Lie theory, American math. monthly,90, 1983.