Endofinite Modules - NALG024

• Title: Endofinitní moduly
• Guaranteed by: Department of Algebra (32-KA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2005
• Semester: winter
• E-Credits: 3
• Hours per week, examination: winter s.:2/0, 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
• Guarantor: Markus Schmidmeier
• Class: Mat. struktury, povinné předměty (blok B); Všeobecné
• Classification: Mathematics > Algebra
• Pre-requisite : NALG028

Annotation

English

An introduction to endofinite modules (modules which have finite length over their endomorphism ring) with applications to representation theory of finite dimensional algebras and to modules over artinian PI-rings.

Last update: G_M (05.10.2001)

Czech

Přednáška v angličtině. An introduction to endofinite modules (modules which have finite length over their endomorphism ring) with applications to representation theory of finite dimensional algebras and to modules over artinian PI-rings.

Last update: ()

Literature

W. Crawley-Boevey, Modules of finite length over their endomorphismring, in: Representations of algebras and related topics, edited by H.Tachikawa and S. Brenner, London Math. Soc. Lect. Notes Series 168, Cambridge University Press, 1992

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

Syllabus

1/ Some basic concepts: Pure injective modules, finite matrix subgroups and the structure of a module over its endomorphismring.

2/ Infinite dimensional modules over finite dimensional algebras: Construction of infinite-dimensional indecomposable modules and their role in the parametrization of finite dimensional modules.

3/ Modules over artinian PI-rings: Duality and Transpose for finite length modules, existence of AR-sequences, as example: variations of the Kronecker-algebra, geometry of their representation space.

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