When stable Cohen-Macaulay Auslander algebra is semisimple

2021/09/01 by Rasool Hafezi, Hafezi, Rasool
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.2109.00467

openalex publication_date 2021/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Gprj-Λ denote the category of Gorenstein projective modules over an Artin algebra Λ and the category mod- (\underlineGprj-Λ) of finitely presented functors over the stable category \underlineGprj-Λ. In this paper, we study those algebras Λ with mod- (\underlineGprj-Λ) to be a semisimple abelian category, and called Ω_G-algebras. The class of Ω_G-algebras contains important classes of algebras, including gentle algebras. Over an Ω_G-algebra Λ, the structure of the almost split sequences in the morphism categories H(Gprj-Λ) and the monomorphism categories S(Gprj-Λ) of Gprj-Λ is investigated. Among other applications, we provide some results for the Cohen-Macaulay Auslander algebras of Ω_G-algebras.

Citations

• On triangulated orbit categories
• Covering theory, (mono)morphism categories and stable Auslander algebras

Related

• G-semisimple algebras
• On Cohen-Macaulay Auslander algebras
• The Auslander-Reiten theory of the morphism category of projective modules
• From subcategories to the entire module categories
• On the stable Auslander-Reiten components of certain monomorphism categories