Higher-dimensional Auslander-Reiten sequences

Jiangsha Li; Jing He

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 3, page 771-786
  • ISSN: 0011-4642

Abstract

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Zhou and Zhu have shown that if 𝒞 is an ( n + 2 ) -angulated category and 𝒳 is a cluster tilting subcategory of 𝒞 , then the quotient category 𝒞 / 𝒳 is an n -abelian category. We show that if 𝒞 has Auslander-Reiten ( n + 2 ) -angles, then 𝒞 / 𝒳 has Auslander-Reiten n -exact sequences.

How to cite

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Li, Jiangsha, and He, Jing. "Higher-dimensional Auslander-Reiten sequences." Czechoslovak Mathematical Journal 74.3 (2024): 771-786. <http://eudml.org/doc/299301>.

@article{Li2024,
abstract = {Zhou and Zhu have shown that if $\mathcal \{C\}$ is an $(n+2)$-angulated category and $\mathcal \{X\}$ is a cluster tilting subcategory of $\mathcal \{C\}$, then the quotient category $\mathcal \{C\}/\mathcal \{X\}$ is an $n$-abelian category. We show that if $\mathcal \{C\}$ has Auslander-Reiten $(n+2)$-angles, then $\mathcal \{C\}/\mathcal \{X\}$ has Auslander-Reiten $n$-exact sequences.},
author = {Li, Jiangsha, He, Jing},
journal = {Czechoslovak Mathematical Journal},
keywords = {$(n+2)$-angulated category; cluster tilting subcategory; $n$-abelian category; Auslander-Reiten $(n+2)$-angle; Auslander-Reiten $n$-exact sequence},
language = {eng},
number = {3},
pages = {771-786},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Higher-dimensional Auslander-Reiten sequences},
url = {http://eudml.org/doc/299301},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Li, Jiangsha
AU - He, Jing
TI - Higher-dimensional Auslander-Reiten sequences
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 771
EP - 786
AB - Zhou and Zhu have shown that if $\mathcal {C}$ is an $(n+2)$-angulated category and $\mathcal {X}$ is a cluster tilting subcategory of $\mathcal {C}$, then the quotient category $\mathcal {C}/\mathcal {X}$ is an $n$-abelian category. We show that if $\mathcal {C}$ has Auslander-Reiten $(n+2)$-angles, then $\mathcal {C}/\mathcal {X}$ has Auslander-Reiten $n$-exact sequences.
LA - eng
KW - $(n+2)$-angulated category; cluster tilting subcategory; $n$-abelian category; Auslander-Reiten $(n+2)$-angle; Auslander-Reiten $n$-exact sequence
UR - http://eudml.org/doc/299301
ER -

References

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