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Classification of higher wide subcategories for higher Auslander algebras of type A

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A subcategory W of an abelian category is called wide if it is closed under kernels, cokernels, and extensions. Wide subcategories are of interest in representation theory because of their links to other homological and combinatorial objects, established among others by Ingalls–Thomas and Marks–Šťovíček. If d⩾1 is an integer, then Jasso introduced the notion of d-abelian categories, where kernels, cokernels, and extensions have been replaced by longer complexes. Wide subcategories can be generalised to this situation. Important examples of d-abelian categories arise as the d-cluster tilting subcategories Mn,d of modAnd−1, where And−1 is a higher Auslander algebra of type A in the sense of Iyama. This paper gives a combinatorial description of the wide subcategories of Mn,d in terms of what we call non-interlacing collections.

Original languageEnglish
Article number106583
JournalJournal of Pure and Applied Algebra
Number of pages22
Publication statusPublished - May 2021

    Research areas

  • d-Abelian category, d-Cluster tilting subcategory, Higher Auslander algebra, Higher homological algebra, Wide subcategory

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