On the Number of τ-Tilting Modules over Nakayama Algebras
Let Λʳₙ be the path algebra of the linearly oriented quiver of type A with n vertices modulo the r-th power of the radical, and let Λ˜ʳₙ be the path algebra of the cyclically oriented quiver of type à with n vertices modulo the r-th power of the radical. Adachi gave a recurrence relation for the num...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210692 |
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| Cite this: | On the Number of τ-Tilting Modules over Nakayama Algebras. Hanpeng Gao and Ralf Schiffler. SIGMA 16 (2020), 058, 13 pages |
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Gao, Hanpeng Schiffler, Ralf 2025-12-15T15:17:33Z 2020 On the Number of τ-Tilting Modules over Nakayama Algebras. Hanpeng Gao and Ralf Schiffler. SIGMA 16 (2020), 058, 13 pages 1815-0659 2020 Mathematics Subject Classification: 16G20; 16G60 arXiv:2002.02990 https://nasplib.isofts.kiev.ua/handle/123456789/210692 https://doi.org/10.3842/SIGMA.2020.058 Let Λʳₙ be the path algebra of the linearly oriented quiver of type A with n vertices modulo the r-th power of the radical, and let Λ˜ʳₙ be the path algebra of the cyclically oriented quiver of type à with n vertices modulo the r-th power of the radical. Adachi gave a recurrence relation for the number of τ-tilting modules over Λʳₙ. In this paper, we show that the same recurrence relation also holds for the number of τ-tilting modules over Λ˜ʳₙ. As an application, we give a new proof for a result by Asai on recurrence formulae for the number of support τ-tilting modules over Λʳₙ and Λ˜ʳₙ. The first author was partially supported by NSFC(GrantNo.11971225). The second author was supported by the NSF grant DMS-1800860 and by the University of Connecticut. The authors also thank the referees for their useful and detailed suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Number of τ-Tilting Modules over Nakayama Algebras Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
On the Number of τ-Tilting Modules over Nakayama Algebras |
| spellingShingle |
On the Number of τ-Tilting Modules over Nakayama Algebras Gao, Hanpeng Schiffler, Ralf |
| title_short |
On the Number of τ-Tilting Modules over Nakayama Algebras |
| title_full |
On the Number of τ-Tilting Modules over Nakayama Algebras |
| title_fullStr |
On the Number of τ-Tilting Modules over Nakayama Algebras |
| title_full_unstemmed |
On the Number of τ-Tilting Modules over Nakayama Algebras |
| title_sort |
on the number of τ-tilting modules over nakayama algebras |
| author |
Gao, Hanpeng Schiffler, Ralf |
| author_facet |
Gao, Hanpeng Schiffler, Ralf |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Let Λʳₙ be the path algebra of the linearly oriented quiver of type A with n vertices modulo the r-th power of the radical, and let Λ˜ʳₙ be the path algebra of the cyclically oriented quiver of type à with n vertices modulo the r-th power of the radical. Adachi gave a recurrence relation for the number of τ-tilting modules over Λʳₙ. In this paper, we show that the same recurrence relation also holds for the number of τ-tilting modules over Λ˜ʳₙ. As an application, we give a new proof for a result by Asai on recurrence formulae for the number of support τ-tilting modules over Λʳₙ and Λ˜ʳₙ.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210692 |
| citation_txt |
On the Number of τ-Tilting Modules over Nakayama Algebras. Hanpeng Gao and Ralf Schiffler. SIGMA 16 (2020), 058, 13 pages |
| work_keys_str_mv |
AT gaohanpeng onthenumberofτtiltingmodulesovernakayamaalgebras AT schifflerralf onthenumberofτtiltingmodulesovernakayamaalgebras |
| first_indexed |
2025-12-17T12:03:39Z |
| last_indexed |
2025-12-17T12:03:39Z |
| _version_ |
1851756925363945472 |