Stable tubes in extriangulated categories

@article{Wang2022,
abstract = {Let $\mathcal \{X\}$ be a semibrick in an extriangulated category. If $\mathcal \{X\}$ is a $\tau $-semibrick, then the Auslander-Reiten quiver $\Gamma (\mathcal \{F\}(\mathcal \{X\}))$ of the filtration subcategory $\mathcal \{F\}(\mathcal \{X\})$ generated by $\mathcal \{X\}$ is $\mathbb \{Z\}\mathbb \{A\}_\{\infty \}$. If $\mathcal \{X\}=\lbrace X_\{i\}\rbrace _\{i=1\}^\{t\}$ is a $\tau $-cycle semibrick, then $\Gamma (\mathcal \{F\}(\mathcal \{X\}))$ is $\mathbb \{Z\}\mathbb \{A\}_\{\infty \}/\tau _\{\mathbb \{A\}\}^\{t\}$.},
author = {Wang, Li, Wei, Jiaqun, Zhang, Haicheng},
journal = {Czechoslovak Mathematical Journal},
keywords = {extriangulated category; semibrick; Auslander-Reiten quiver},
language = {eng},
number = {3},
pages = {765-782},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stable tubes in extriangulated categories},
url = {http://eudml.org/doc/298371},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Wang, Li
AU - Wei, Jiaqun
AU - Zhang, Haicheng
TI - Stable tubes in extriangulated categories
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 3
SP - 765
EP - 782
AB - Let $\mathcal {X}$ be a semibrick in an extriangulated category. If $\mathcal {X}$ is a $\tau $-semibrick, then the Auslander-Reiten quiver $\Gamma (\mathcal {F}(\mathcal {X}))$ of the filtration subcategory $\mathcal {F}(\mathcal {X})$ generated by $\mathcal {X}$ is $\mathbb {Z}\mathbb {A}_{\infty }$. If $\mathcal {X}=\lbrace X_{i}\rbrace _{i=1}^{t}$ is a $\tau $-cycle semibrick, then $\Gamma (\mathcal {F}(\mathcal {X}))$ is $\mathbb {Z}\mathbb {A}_{\infty }/\tau _{\mathbb {A}}^{t}$.
LA - eng
KW - extriangulated category; semibrick; Auslander-Reiten quiver
UR - http://eudml.org/doc/298371
ER -