Article
| Title: | Stable tubes in extriangulated categories (English) |
| Author: | Wang, Li |
| Author: | Wei, Jiaqun |
| Author: | Zhang, Haicheng |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 3 |
| Year: | 2022 |
| Pages: | 765-782 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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 $\mathcal {X}=\{X_{i}\}_{i=1}^{t}$ is a $\tau $-cycle semibrick, then $\Gamma (\mathcal {F}(\mathcal {X}))$ is $\mathbb {Z}\mathbb {A}_{\infty }/\tau _{\mathbb {A}}^{t}$. (English) |
| Keyword: | extriangulated category |
| Keyword: | semibrick |
| Keyword: | Auslander-Reiten quiver |
| MSC: | 18E05 |
| idZBL: | Zbl 07584101 |
| idMR: | MR4467941 |
| DOI: | 10.21136/CMJ.2022.0145-21 |
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| Date available: | 2022-08-22T08:22:17Z |
| Last updated: | 2022-12-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150616 |
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| Reference: | [1] Gorsky, M., Nakaoka, H., Palu, Y.: Positive and negative extensions in extriangulated categories.Available at https://arxiv.org/abs/2103.12482 (2021), 51 pages. |
| Reference: | [2] Iyama, O., Nakaoka, H., Palu, Y.: Auslander-Reiten theory in extriangulated categories.Available at https://arxiv.org/abs/1805.03776 (2019), 40 pages. |
| Reference: | [3] Nakaoka, H., Palu, Y.: Extriangulated categories, Hovey twin cotorsion pairs and model structures.Cah. Topol. Géom. Différ. Catég. 60 (2019), 117-193. Zbl 1451.18021, MR 3931945 |
| Reference: | [4] Ringel, C. M.: Tame Algebras and Integral Quadratic Forms.Lecture Notes in Mathematics 1099. Springer, Berlin (1984). Zbl 0546.16013, MR 0774589, 10.1007/BFb0072870 |
| Reference: | [5] Simson, D., Skowroński, A.: Elements of the Representation Theory of Associative Algebras. Vol. 2. Tubes and Concealed Algebras of Euclidean Type.London Mathematical Society Student Texts 71. Cambridge University Press, Cambridge (2007). Zbl 1129.16001, MR 2360503, 10.1017/CBO9780511619212 |
| Reference: | [6] Wang, L., Wei, J., Zhang, H.: Semibricks in extriangulated categories.Commun. Algebra 49 (2021), 5247-5262. Zbl 07431295, MR 4328535, 10.1080/00927872.2021.1940192 |
| Reference: | [7] Zhou, P., Zhu, B.: Triangulated quotient categories revisited.J. Algebra 502 (2018), 196-232. Zbl 1388.18014, MR 3774890, 10.1016/j.jalgebra.2018.01.031 |
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