| Area of Mathematics: | Algebra & Geometry (EAG) | ||
| Semester: | 8ο | ||
| Course ID: | 82203 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | |||
| Instructors: |
Description
- Lie groups (continuous groups, infinitesimal generators, the orthogonal group O(3), the SU(2) groups.
- Lie algebras (simple and semi-simple Lie algebras, Lie and Engels theorems, Casimir tensor).
- Representations of Lie groups and algebras.
- The exponential map of a Lie group.
- Classic Lie algebras. Matrix algebras.
- Dynkin diagrams and classification of semi-simple Lie algebras.
- Differential geometry and Lie groups.
- Symmetry groups in differential equations.
- Invariant forms over Lie groups.
Bibliography
- Gilmore R., Lie Groups, Lie Algebras, and some of their Applications, Dover, 2006.
- Hall B., Lie Groups, Lie Algebras, and Representations, Springer, 2nd ed., 2015.
