Cohen-Macaulay Auslander algebras of gentle algebras

2015/02/13 by Xinhong Chen, Ming Lu, Chen, Xinhong +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1502.03948

openalex publication_date 2015/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any gentle algebra Λ=KQ/⟨ I⟩, following Kalck, we describe the quiver and the relations for its Cohen-Macaulay Auslander algebra Aus(GprojΛ) explicitly, and obtain some properties, such as Λ is representation-finite if and only if Aus(GprojΛ) is; if Q has no loop and any indecomposable Λ-module is uniquely determined by its dimension vector, then any indecomposable Aus(GprojΛ)-module is uniquely determined by its dimension vector.

Citations

• Perverse equivalences, BB-tilting, mutations and applications
• Gentle algebras arising from surface triangulations
• On triangulated orbit categories

Cited by

• On Cohen-Macaulay Auslander algebras
• On BD-algebra and CM-Auslander algebra for a gentle algebra and their representation types
• Desingularization of quiver Grassmannians for Gentle algebras

Related

• On endomorphism algebras of string almost gentle algebras
• The Cohen-Macaulay Auslander algebras of string algebras
• On Cohen-Macaulay Auslander algebras
• Desingularization of quiver Grassmannians for Gentle algebras
• On BD-algebra and CM-Auslander algebra for a gentle algebra and their representation types