Modular Group Representations - NALG023
Title: Modulární reprezentace grup
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2005
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: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Markus Schmidmeier
Class: Mat. struktury, povinné předměty (blok B)
Všeobecné
Classification: Mathematics > Algebra
Co-requisite : NALG028
Pre-requisite : NALG001, NALG002
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Annotation -
In this course we study the operation of finite groups on K-vectorspaces, this is to say we study modules over group algebras. Of particular interest is the case that the characteristic p of K divides the order of the group.
Last update: G_M (05.10.2001)
Literature - Czech

J.L.Alperin, Local representation theory, Cambridge studies in advanced mathematics 11, Cambridge University Press,1986

Last update: Zakouřil Pavel, RNDr., Ph.D. (05.08.2002)
Syllabus - Czech

1/ Semisimple modules: Basic results about modules, Maschke's theorem and formula for the number of isoclasses of simple KG-modules.

2/ Projective modules: Decomposition of modules, structure of the projective indecomposable modules and as example: the group of invertible 2x2-matrices over the field with p elements.

3/ Modules over subgroups: Restriction and induction, relative projective modules and the Green-correspondence.

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