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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
Teaching methods:	full-time

Guarantor:	doc. RNDr. Jan Šťovíček, Ph.D.
Classification:	Mathematics > Algebra
Interchangeability :	NMAG442
Is incompatible with:	NMAG442
Is interchangeable with:	NMAG442

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KA (19.05.2009)

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 (19.05.2009)

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 (19.05.2009)

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 (19.05.2009)

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