(in Polish) Representation theory of finite dimensional algebras II 1000-M2RepTheory2

Module III

Quivers and their representations

1. Quivers and path algebras
2. Admissible ideals and quotients of the path algebra
3. The quiver of a finite dimensional algebra
4. Representations of bound quivers
5. The simple projective, and injective modules
6. Quivers of finite representation type
7. Integral quadratic forms
8. The quadratic form of a quiver
9. Coxeter functors

Passing the course: oral examination.

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 bound quiver algebra and their representations, a quiver of a finite dimensional algebra, a quadratic form of a quiver, a finite representation type, an infinite representation type, 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 quivers of finite representation type and quivers of infinite representation type and write down for a given quiver its simple, projective and injective representations. (P8S_UW)

Expository teaching methods

- informative (conventional) lecture

Prerequisites

Linear algebra, Algebra I and Representation theory of finite dimensional algebras 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.

Additional information

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

Description of 1000-M2RepTheory2 in USOSweb