Elements of group theory 0800-ELEGRUP

Lecture schedule:

1) Finite groups
- basic definitions
- examples

2) Representation theory
- irreducible representations
- Schur theorem
- orthogonality relations

3) Lie algebras
- classification of algebras
- Killing's tensor
- algebras representations

4) Matrix groups and algebras

5) Orthogonal group O (2) and SO (2):
-structure of irreducible representations

6) rotation group SO(3)
- parameterizations of SO(3)
- topology of SO(3)
- Lie algebra so(3) - angular momentum
- structure of irreducible representations of SO(3) group

7) Unitary group SU(2)
- parameterization of SU(2)
- Lie algebra su(2)
- structure of irreducible representations
- relationship between SO(3) and SU(2)

8) The Lorentz group and Poincare
- commutation relations
- basic information about representations