After successful completion of the course, students are able to explain basic concepts about Lie algebras (ideals, nilpotent, solvable, semisimple Lie algebras, ...). They can formulate and prove the theorems of Engel, Lie as well as the criteria of Cartan and the theorem of Weyl. Moreover, students are able to show that the set of roots of a semisimple Lie algebra forms an abstract root system.
Lie algebras, ideals and homomorphisms; Theorems of Lie and Engel, Cartan's criteria; Root space decompositions of semisimple Lie algebras; Representations, Theorem of Weyl; Root systems
Mathematical definitions and proofs
Vorbesprechung: Dienstag, 3. März, 14 UhrOrt: Besprechungszimmer, Wiedner Hauptstraße 8-10, 1040 Wien, Turm A, 7.Stock, grüner Bereich
Blackboard presentations and active participation during the whole semester.
