# A characterization of representation infinite quiver settings

## TL;DR

This paper characterizes quiver and dimension vector pairs that admit infinitely many representations over algebraically closed fields, providing insights into the structure of such representations and their orbit classifications.

## Contribution

It offers a new characterization of representation-infinite quiver settings and applies this to the study of algebraic orbit finiteness.

## Key findings

- Identifies conditions for infinite representation types
- Links representation theory to orbit classification
- Provides criteria for finiteness of orbits

## Abstract

We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this result to the study of algebras with finitely many orbits with respect to the action of (the double product) of the group of units.