*Conducted in term:*2024/25Z

*ECTS credits:*3

*Language:*English

*Organized by:*Faculty of Mathematics and Computer Science

# (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

## Learning outcomes - knowledge

## Learning outcomes - skills

## Expository teaching methods

## Prerequisites

## Course coordinators

## 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: