2021/09/02 by Zongzhen Xie, Xie, Zongzhen, Xiaojin Zhang +1
Mathematics · Medicine · Physics and Astronomy · #16G10 #18G25 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2109.01248
openalex publication_date 2021/09/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We introduce the notions of Gorenstein projective τ-rigid modules, Gorenstein projective support τ-tilting modules and Gorenstein torsion pairs and give a Gorenstein analog to Adachi-Iyama-Reiten's bijection theorem on support τ-tilting modules. More precisely, for an algebra Λ, We prove that there is a bijection between the set of Gorenstein projective support τ-tilting modules and the set of functorially finite Gorenstein projective torsion classes. As an application, we introduce the notion of CM-τ-tilting finite algebras and show that Λ is CM-τ-tilting finite if and only if Λ^\rm op is CM-τ-tilting finite. Moreover, we show that the Bongartz completion of a Gorenstein projective τ-rigid module need not be a Gorenstein projective τ-tilting module.