(in Polish) Representation theory of finite dimensional algebras I 1000-M2RepTheory1

Module I

Algebras, modules and categories

1. Terminology and notations
2. Categories and functors
3. Simple modules, radical and semisimple algebras
4. Direct sum decompositions
5. Projective modules and injective modules
6. Basic algebras and embeddings of module categories
7. Grothendieck group
8. Fibered product and fibered sum of modules
9. Extensions of finite dimensional modules

Passing the course: oral examination.

Class dates: Tuesdays 2:15 - 4:00 p.m., room S2, Faculty of Mathematics and Computer Science, Chopina 12/18

Total student workload

30 hours - lecture 30 hours - individual work: preparation for classes and studying literature 30 hours - individual work: preparation for the exam

Learning outcomes - knowledge

After completing the course, the doctoral student knows the concept of a category, a functor, a module, a projective module, an injective module, a Grothendieck group, as well as the most important theorems concerning them. (P8S_WG)

Learning outcomes - skills

After completing the course, the doctoral student is able to give examples of categories, functors, knows the basic properties of projective modules, injective modules and knows the theorem on the uniqueness of the decomposition of any module over a finite-dimensional algebra. (P8S_UW)

Expository teaching methods

- informative (conventional) lecture

Prerequisites

Linear algebra, Algebra I

Course coordinators

Piotr Malicki

Bibliography

Basic literature:

I. Assem, D. Simson and A. Skowroński,
"Elements of the Representation Theory of Associative Algebras 1: Techniques of Representation Theory", London Mathematical Society Student Texts 65, Cambridge University Press, Cambridge, 2006.

A. Skowroński, K. Yamagata, "Frobenius algebras. I: Basic representation theory", EMS Textbooks in Mathematics. Zürich: European Mathematical Society (EMS), 2011.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1000-M2RepTheory1 in USOSweb