
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
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. FrobeniusScur 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. 

