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Course, academic year 2017/2018
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Group Representations 1 - NMAG438
Czech title: Reprezentace grup 1
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017 to 2017
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: 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: doc. Mgr. Pavel Příhoda, Ph.D. (02.03.2018)

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: doc. Mgr. Pavel Příhoda, Ph.D. (02.03.2018)

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.

 
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