Stable Brauer-Thrall II' conjecture for finite-dimensional Jacobian algebras

TL;DR

This paper proves that finite-dimensional Jacobian algebras from non-degenerate quivers with potentials satisfy the stable Brauer-Thrall II' conjecture, confirming related conjectures for these algebras.

Contribution

It establishes the validity of the stable Brauer-Thrall II' conjecture for a broad class of Jacobian algebras, advancing understanding in representation theory.

Findings

Proves the stable Brauer-Thrall II' conjecture for Jacobian algebras.

Confirms the brick Brauer-Thrall II' conjecture for these algebras.

Links properties of quivers with potentials to algebraic conjectures.

Abstract

We prove that finite-dimensional Jacobian algebras associated with non-degenerate quivers with potentials satisfy the stable Brauer-Thrall II' conjecture. In particular, this implies that the brick Brauer-Thrall II' conjecture (also known as the $\tau$-Brauer-Thrall II' conjecture) holds for finite-dimensional Jacobian algebras.