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

2025/12/07 by Haerizadeh, Mohamad, Yurikusa, Toshiya
Mathematics · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics

paper · doi:10.48550/arxiv.2512.06623

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 τ-Brauer-Thrall II' conjecture) holds for finite-dimensional Jacobian algebras.

Citations

• Finite-dimensional Jacobian algebras: Finiteness and tameness
• Semistable torsion classes and canonical decompositions in Grothendieck groups
• τ-Tilting Finiteness of Non-distributive Algebras and their Module Varieties
• The wall-chamber structures of the real Grothendieck groups
• Tilting-connected symmetric algebras
• Quivers with potentials associated to triangulated surfaces
• Quivers with potentials and their representations I: Mutations
• Recognizing Cluster Algebras of Finite type

Related

• On finite dimensional Jacobian Algebras
• Hom-orthogonal modules and brick-Brauer-Thrall conjectures
• On the bricks (Schur representations) of finite dimensional algebras
• Finite-dimensional Jacobian algebras: Finiteness and tameness
• Remarks on τ-tilted versions of the second Brauer-Thrall Conjecture