Auslander Reiten Quivers
Date:
An overview of Auslander Reiten quivers and why they are useful.
A talk for the Bristol Junior Algebra Colloquium.
Abstract
When studying algebraic objects, it is often beneficial to focus your attention on a class of “least complicated” objects that you can use to build the rest of the objects. In the representation theory of algebras, one useful notion of “least complicated” objects is that of indecomposable modules.
The Auslander-Reiten quiver is a construction to encode information about morphisms between indecomposable modules. The combinatorial properties of this quiver are useful in understanding the morphisms between arbitrary modules of the algebra.
I will begin with an introduction to both algebras over a field, and their relation to quivers, and use this to illustrate an example of the Auslander-Reiten quiver.
(Slides)