Representation Theory of Finite-dimensional Algebras - NALG022
Title: Teorie reprezentací konečně-dimenzionálních algeber
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/1, 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
Guarantor: doc. RNDr. Jan Šťovíček, Ph.D.
Classification: Mathematics > Algebra
Interchangeability : NMAG442
Is incompatible with: NMAG442
Is interchangeable with: NMAG442
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Annotation -
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.
Last update: T_KA (19.05.2009)
Literature -
  • 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.

Last update: T_KA (19.05.2009)
Syllabus -

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.

Last update: T_KA (19.05.2009)
Entry requirements -

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

Last update: T_KA (19.05.2009)