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

Martin Herschend; Peter Jørgensen

doi:10.1016/j.jpaa.2020.106583

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

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Department of Mathematics

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Abstract

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is an integer, then Jasso introduced the notion of d-abelian categories, where kernels, cokernels, and extensions have been replaced by longer complexes.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 M_n,d of modA_n^d−1, where A_n^d−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 M_n,d in terms of what we call non-interlacing collections.

Original language	English
Article number	106583
Journal	Journal of Pure and Applied Algebra
Volume	225
Issue	5
Number of pages	22
ISSN	0022-4049
DOIs	https://doi.org/10.1016/j.jpaa.2020.106583
Publication status	Published - May 2021

Keywords

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

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10.1016/j.jpaa.2020.106583

https://arxiv.org/pdf/2002.01778.pdf

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title = "Classification of higher wide subcategories for higher Auslander algebras of type A",

abstract = "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–{\v S}{\v t}ov{\'i}{\v c}ek. 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is an integer, then Jasso introduced the notion of d-abelian categories, where kernels, cokernels, and extensions have been replaced by longer complexes.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.",

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author = "Martin Herschend and Peter J{\o}rgensen",

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doi = "10.1016/j.jpaa.2020.106583",

language = "English",

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journal = "Journal of Pure and Applied Algebra",

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AU - Herschend, Martin

AU - Jørgensen, Peter

PY - 2021/5

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N2 - 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.

AB - 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.

KW - d-Abelian category

KW - d-Cluster tilting subcategory

KW - Higher Auslander algebra

KW - Higher homological algebra

KW - Wide subcategory

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DO - 10.1016/j.jpaa.2020.106583

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SN - 0022-4049

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

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ER -

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

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Keywords

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