SubjectsSubjects(version: 835)
Course, academic year 2018/2019
   Login via CAS
Group Representations 1 - NMAG438
Title in English: Reprezentace grup 1
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: English, Czech
Teaching methods: full-time
Guarantor: doc. Mgr. Pavel Příhoda, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG021
Interchangeability : NALG021
Annotation -
Last update: T_KA (14.05.2013)

Elements of theory of representations of groups.
Course completion requirements -
Last update: T_KA (14.05.2013)

Several homeworks will be given during the course. To get the credits for problem sessions it will be sufficient to solve three of them.

Literature -
Last update: T_KA (14.05.2013)

1. Charles W. Curtis, Irving Reiner: Representation theory of finite groups and associative algebras, John Wiley & Sons, New York, 1988.

2. Walter Feit: The representation theory of finite groups, North-Holland mathematical library, Amsterdam, 1982

3. Steven H. Weintraub: Representation Theory of Finite Groups: Algebra and Arithmetic (Graduate Studies in Mathematics, Vol. 59), AMS, Providence 2003.

Requirements to the exam -
Last update: T_KA (14.05.2013)

The exam consists of three questions. Two of them are theoretical (definitions, theorems and proofs) and one of them is more practical

(for example calculate character table of a given group).

Syllabus -
Last update: T_KA (14.05.2013)

1/ Irreducible representations of groups, Shur's Lemma.

2/ Representations as modules over group rings, direct sum and tensor product of representations.

3/ Representations of finite groups, Maschke's Theorem.

4/ Characters, orthogonality relations, Burnside's theorem.

5/ Rank of irreducible representations.

6/ Representations over the field of complex numbers and irreducible characters.

7/ Permutation representations.

8/ Representations induced by subgroups of finite index.

9/ Projective representations; Shur's multiplier.

10/ Applications in probability theory.

Charles University | Information system of Charles University |