2019/01/25 by Joseph L. Reid, Reid, Joseph
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1901.08953
openalex publication_date 2019/01/25 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
Let mathscrC be a 2-Calabi-Yau triangulated category, and let\n mathscrT be a cluster tilting subcategory of mathscrC. An important\nresult from Dehy and Keller tells us that a rigid object c \∈ mathscrC is\nuniquely defined by its index with respect to mathscrT.\n The notion of triangulated categories extends to the notion of\n(d+2)-angulated categories. Thanks to a paper by Oppermann and Thomas, we now\nhave a definition for cluster tilting subcategories in higher dimensions. This\npaper proves that under a technical assumption, an indecomposable object in a\n(d+2)-angulated category is uniquely defined by its index with respect to a\nhigher dimensional cluster tilting subcategory. We also demonstrate an\napplication of this result in higher dimensional cluster categories.\n