REPRESENTATION THEORY OF GROUPS

Second cycle degree in MATHEMATICS

Campus: PADOVA

Language: English

Teaching period: Second Semester

Lecturer: GIOVANNA CARNOVALE

Number of ECTS credits allocated: 6


Syllabus
Prerequisites: Basic notions in linear algebra and group theory.
Examination methods: Written, involving a series of exercises.
Course unit contents: Representations. Irreducible representations. Maschke's theorem. Orthogonality of characters. Induced representations. Frobenius reciprocity. Rappresentazioni Indotte, formual di Mackey. Reciprocita' di Frobenius. Frobenius-Scur Indicator. Compact groups. Linear algebraic groups and their Lie algebras. Solvable, nilpotent and semisimple Lie algebras. Cartan's criterion. Killing form. Weyl's theorem. Root space decomposition. Root systems. Classification of semisimple Lie algebras. Universal enveloping algebras. Finite dimensional irreducible representations of a semisimple Lie algebra.