The stable category of Gorenstein-projective modules over a monomial algebra

2024/07/06 by Takahiro Honma, Honma, Takahiro, Satoshi Usui +1 · 1 citation
Mathematics · #16G20 #16G50 #16G70 #18G80 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2407.04912

openalex publication_date 2024/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Λ be an arbitrary monomial algebra. We investigate the stable category \underlineGproj^ℤΛ of graded Gorenstein-projective Λ-modules and the orbit category \underlineGproj^ℤ Λ/(1) induced by \underlineGproj^ℤΛ and the degree shift functor (1). We prove that \underlineGproj^ℤΛ is triangle equivalent to the bounded derived category of a path algebra of Dynkin type \mathbbA and that \underlineGproj^ℤΛ/(1) is triangle equivalent to the stable module category of a self-injective Nakayama algebra. Both the path algebra and the self-injective Nakayama algebra will be given explicitly. The latter result provides an explicit description of the stable category of (ungraded) Gorenstein-projective Λ-modules.

Cited by

• Gorenstein-Projective Modules over the Ring of Dual Integers

Related

• The Gorenstein-projective modules over a monomial algebra
• Realizing stable categories as derived categories
• From Gorenstein derived equivalences to stable functors of Gorenstein projective modules
• Invariants and Gorenstein projective modules
• Homological theory of orthogonal modules