SUBJECT
Group theory
lecture
master
2
Semester 1
Autumn semester
Group and homomorphism. Subgroups, cosets, normal subgroups and factor groups. Products of groups. Conjugacy classes, centralizers and derived subgroups. Elements of mathematical crystallography.
Lie groups: topological properties, Lie algebras and Haar measure. Representations and covering groups. The rotation group.
Group actions: orbits and stabilizers, classification of transitive actions, operations on actions.
Group representations: irreducibility, Schur's lemma, direct sums and tensor products, branching rules, characters and orthogonality relations, projective representations, symmetrized products, Frobenius-Schur indicators, induced representations and the reciprocity theorem, polynomial invariants.
Group presentations: free groups, Nielsen-Schreier theorem, generators and relations, Tietze transformations.
- Alperin-Bell: Groups and representations (Springer, 1995)
- Robinson: A Course in the Theory of Groups (Springer, 1995)
- Kirillov: Elements of the theory of representations (Springer, 1976)