Quivers and Poisson structures

TL;DR

This paper introduces natural quadratic Poisson structures on moduli spaces of quiver representations, focusing on the generalized Kronecker quiver with three arrows, expanding the understanding of geometric structures in representation theory.

Contribution

It constructs and analyzes quadratic Poisson structures on moduli spaces of quiver representations, especially for the generalized Kronecker quiver with three arrows, a novel application in the field.

Findings

Quadratic Poisson structures are constructed on moduli spaces.

A specific Poisson structure for the generalized Kronecker quiver with 3 arrows is studied.

The work provides new insights into the geometric structures of quiver moduli spaces.

Abstract

We produce natural quadratic Poisson structures on moduli spaces of representations of quivers. In particular, we study a natural Poisson structure for the generalised Kronecker quiver with 3 arrows.