Expander representations of quivers

TL;DR

This paper introduces expander representations of quivers, extending the concept of linear algebra expanders, and proves their existence for any wild quiver over an algebraically closed field using spectral analysis.

Contribution

It defines a new class of quiver representations called expander representations and establishes their existence for all wild quivers, linking stability and spectral properties.

Findings

Existence of uniform expander representations for wild quivers.

Connection between expander representations and spectral properties of Cartan matrices.

Generalization of dimension expanders to quiver settings.

Abstract

We propose a definition of expander representations of quivers, generalizing dimension (or linear algebra) expanders, as a qualitative refinement of slope stability. We prove existence of uniform expander representations for any wild quiver over an algebraically closed base field, using the concept of general subrepresentations and spectral properties of Cartan matrices.