n-abelian quotient categories

2018/07/18 by Panyue Zhou, Bin Zhu, Zhou, Panyue +1
Mathematics · Physics and Astronomy · #18E10 #18E30 #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.1807.06733

openalex publication_date 2018/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \C be an (n+2)-angulated category with shift functor Σ and \X be a cluster-tilting subcategory of \C. Then we show that the quotient category \C/\X is an n-abelian category. If \C has a Serre functor, then \C/\X is equivalent to an n-cluster tilting subcategory of an abelian category \textrmmod(Σ^-1\X). Moreover, we also prove that \textrmmod(Σ^-1\X) is Gorenstein of Gorenstein dimension at most n. As an application, we generalize recent results of Jacobsen-Jørgensen and Koenig-Zhu.

Citations

• The triangulation of the subfactor categories of additive categories with suspensions

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