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Group Representations 1 - NMAG438

Title:	Reprezentace grup 1
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2016
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	English, Czech
Teaching methods:	full-time
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
Is interchangeable with:	NALG021

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (14.05.2019)

Elements of theory of representations of groups.

Literature -

Last update: doc. RNDr. David Stanovský, Ph.D. (17.02.2024)

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.

Syllabus -

Last update: doc. RNDr. David Stanovský, Ph.D. (17.02.2024)

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.