The QuiverTools package for SageMath and Julia

2025/06/24 by Belmans, Pieter, Franzen, Hans, Petrella, Gianni · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2506.19432

Abstract

We introduce QuiverTools, a new software package, available in both a SageMath and Julia version, to study quivers and their moduli spaces of representations. Its key features are the computation of general subdimension vectors, leading to canonical decompositions, and checking the existence of (semi)stable representations, as well as the enumeration of Harder-Narasimhan types and related calculations for Teleman quantization. Computations related to intersection theory on quiver moduli are also implemented.

Citations

• Full Exceptional Sequence for a Fine Quiver Moduli Space
• Rigidity and Schofield's partial tilting conjecture for quiver moduli
• On Chow rings of quiver moduli
• Kac polynomials and Lie algebras associated to quivers and curves
• Julia: A Fresh Approach to Numerical Computing
• Julia: A Fresh Approach to Numerical Computing
• Stratifications for moduli of sheaves and moduli of quiver representations
• The derived category of a GIT quotient
• Moduli of representations of quivers

Cited by

• Finding the walls for quiver moduli

Related

• Lecture Notes on Quiver Representations and Moduli Problems in Algebraic Geometry
• Moduli of representations of quivers
• Completely-decomposable subcategories of quiver representations
• Some algorithms for semi-invariants of quivers
• Representations of marked quivers