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Course, academic year 2017/2018
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Representation Theory of Finite-Dimensional Algebras - NMAG442
Czech title: Teorie reprezentací konečně-dimenzionálních algeber
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Guarantor: doc. RNDr. Jan Šťovíček, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG022
Interchangeability : NALG022
Annotation -
Last update: T_KA (14.05.2013)

The lecture is meant as an introduction to representation theory of finite dimensional algebras. The focus is put on path algebras, Auslander-Reiten theory, representation types and basics of tilting theory.
Literature -
Last update: T_KA (14.05.2013)

  • I. Assem, D. Simson and A. Skowroński, Elements of the Representation Theory of Associative Algebras I, Cambridge University Press, 1997.
  • M. Auslander, I. Reiten and S. O. Smalo, Representation Theory of Artin Algebras, Cambridge University Press, 2006.

Syllabus -
Last update: T_KA (14.05.2013)

1. Path algebras, representations of quivers as modules over path algebras.

2. Projective and injective modules, indecomposable modules, Krull-Schmidt theorem.

3. Irreducible morphisms and almost split sequences, Auslander-Reiten quiver.

4. Finite representation type, the first Brauer-Thrall conjecture.

5. Representations of hereditary algebras, Gabriel's theorem.

6. Tilting and cotilting modules.

Entry requirements -
Last update: T_KA (14.05.2013)

Basics of theory of modules (to the extent of lecture NALG028) and basic homological algebra (the Ext functor).

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