
Course unit
REPRESENTATION THEORY OF GROUPS
SC01120635, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/02 
Algebra 
6.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
2.0 
16 
34.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
Examination board
Examination board not defined
Prerequisites:

Basic notions in linear algebra and group theory. 
Target skills and knowledge:

The student will learn the basic notions on complex representations of finite groups and the classification of complex semisimple Lie algebras. 
Examination methods:

Written exam 
Assessment criteria:

Exams will be evaluated on basis of their completeness, correctness and exactness. 
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. 
Planned learning activities and teaching methods:

Classroom lectures. In the course webpage students can find exercises to solve. 
Additional notes about suggested reading:

We will also use a few pages from these Lecture Notes by Alexander Kleschchev
http://darkwing.uoregon.edu/~klesh/teaching/AGLN.pdf 
Textbooks (and optional supplementary readings) 


