Universal Deformation Rings and Quivers of Finite Representation Type

TL;DR

This paper proves that for quivers of finite representation type over any field, the universal deformation ring of an indecomposable module is always isomorphic to the base field, revealing a fundamental property of such modules.

Contribution

It establishes that the universal deformation rings of indecomposable modules over finite type quivers are always isomorphic to the base field, regardless of characteristic.

Findings

Universal deformation rings of indecomposable modules are isomorphic to the base field

The result holds over fields of arbitrary characteristic

Provides a fundamental understanding of module deformations in finite type quivers

Abstract

Let k be a field of arbitrary characteristic and let Q be a quiver of finite representation type. In this paper we prove that if M is an indecomposable kQ-module then the universal deformation ring of M over kQ is isomorphic to k.