Stable tubes in extriangulated categories
Li Wang; Jiaqun Wei; Haicheng Zhang
Czechoslovak Mathematical Journal (2022)
- Volume: 72, Issue: 3, page 765-782
- ISSN: 0011-4642
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topWang, Li, Wei, Jiaqun, and Zhang, Haicheng. "Stable tubes in extriangulated categories." Czechoslovak Mathematical Journal 72.3 (2022): 765-782. <http://eudml.org/doc/298371>.
@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 -
References
top- Gorsky, M., Nakaoka, H., Palu, Y., Positive and negative extensions in extriangulated categories, Available at https://arxiv.org/abs/2103.12482 (2021), 51 pages. (2021)
- Iyama, O., Nakaoka, H., Palu, Y., Auslander-Reiten theory in extriangulated categories, Available at https://arxiv.org/abs/1805.03776 (2019), 40 pages. (2019)
- Nakaoka, H., Palu, Y., Extriangulated categories, Hovey twin cotorsion pairs and model structures, Cah. Topol. Géom. Différ. Catég. 60 (2019), 117-193. (2019) Zbl1451.18021MR3931945
- Ringel, C. M., 10.1007/BFb0072870, Lecture Notes in Mathematics 1099. Springer, Berlin (1984). (1984) Zbl0546.16013MR0774589DOI10.1007/BFb0072870
- Simson, D., Skowroński, A., 10.1017/CBO9780511619212, London Mathematical Society Student Texts 71. Cambridge University Press, Cambridge (2007). (2007) Zbl1129.16001MR2360503DOI10.1017/CBO9780511619212
- Wang, L., Wei, J., Zhang, H., 10.1080/00927872.2021.1940192, Commun. Algebra 49 (2021), 5247-5262. (2021) Zbl07431295MR4328535DOI10.1080/00927872.2021.1940192
- Zhou, P., Zhu, B., 10.1016/j.jalgebra.2018.01.031, J. Algebra 502 (2018), 196-232. (2018) Zbl1388.18014MR3774890DOI10.1016/j.jalgebra.2018.01.031
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