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Group Representations 2 - NMAG567

Title:	Reprezentace grup 2
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time

Guarantor:	doc. Mgr. Pavel Příhoda, Ph.D.
Teacher(s):	doc. Mgr. Pavel Příhoda, Ph.D.
Class:	M Mgr. MSTR M Mgr. MSTR > Volitelné
Classification:	Mathematics > Algebra
Incompatibility :	NALG124
Interchangeability :	NALG124
Is interchangeable with:	NALG124

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Annotation -

The course gives a brief overview of some classical results on modular and integral representations of finite groups.

Last update: T_KA (14.05.2013)

Course completion requirements - Czech

Zápočet bude udělen buď za průběžné řešení úloh ze cvičení nebo za vyřešení sady domácích úkolů, které zadám ke konci semestru.

Last update: Příhoda Pavel, doc. Mgr., Ph.D. (13.10.2023)

Literature -

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.

Last update: T_KA (14.05.2013)

Requirements to the exam - Czech

Zkouška bude ústní - dvě otázky z probrané látky. K úspěšnému složení zkoušky stačí prokázat základní přehled u každé otázky.

Last update: Příhoda Pavel, doc. Mgr., Ph.D. (13.10.2023)

Syllabus -

The course is a free continuation of Group Representations 1. It can also cover topics from the previous course.

1. Discrete Fourier transform on finite groups and its applications.

2. Induced representations, theorems of Artin and Brauer.

3. Introduction to modular representation of finite groups. Brauer characters, finite representation type.

4. (probably only some of these topics) Projective representations, lattices, vertices and sources.

Last update: Příhoda Pavel, doc. Mgr., Ph.D. (09.09.2024)