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

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Classification of higher wide subcategories for higher Auslander algebras of type A. / Herschend, Martin; Jørgensen, Peter.

I: Journal of Pure and Applied Algebra, Bind 225, Nr. 5, 106583, 05.2021.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Herschend, Martin ; Jørgensen, Peter. / Classification of higher wide subcategories for higher Auslander algebras of type A. I: Journal of Pure and Applied Algebra. 2021 ; Bind 225, Nr. 5.

Bibtex

@article{93456787299a4e4489914ac12b5d55bd,
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is an integer, then Jasso introduced the notion of d-abelian categories, where kernels, cokernels, and extensions have been replaced by longer complexes.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.",
keywords = "d-Abelian category, d-Cluster tilting subcategory, Higher Auslander algebra, Higher homological algebra, Wide subcategory",
author = "Martin Herschend and Peter J{\o}rgensen",
year = "2021",
month = may,
doi = "10.1016/j.jpaa.2020.106583",
language = "English",
volume = "225",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier BV * North-Holland",
number = "5",

}

RIS

TY - JOUR

T1 - Classification of higher wide subcategories for higher Auslander algebras of type A

AU - Herschend, Martin

AU - Jørgensen, Peter

PY - 2021/5

Y1 - 2021/5

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

UR - http://www.scopus.com/inward/record.url?scp=85092689982&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2020.106583

DO - 10.1016/j.jpaa.2020.106583

M3 - Journal article

AN - SCOPUS:85092689982

VL - 225

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 5

M1 - 106583

ER -