2020/04/05 by Laertis Vaso, Vaso, Laertis · 1 citation
Mathematics · #16G20 (Primary) 16G70 #18E10 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2004.02269
openalex publication_date 2020/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new way to construct n-cluster tilting subcategories of abelian categories. Our method takes as input a direct system of abelian categories Ai with certain subcategories and, under reasonable conditions, outputs an n-cluster tilting subcategory of an admissible target A of the direct system. We apply this general method to a direct system of module categories modΛi of representation-directed algebras Λi and obtain an n-cluster tilting subcategory M of a module category modC of a locally bounded Krull-Schmidt category C. In certain cases we also construct an admissible ℤ-action of C. Using a result of Darpö-Iyama, we obtain an n-cluster tilting subcategory of mod(C/ℤ) where C/ℤ is the corresponding orbit category. We show that in this case mod(C/ℤ) is equivalent to the module category of a finite-dimensional algebra. In this way we construct many new families of representation-finite algebras whose module categories admit n-cluster tilting modules.