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 |
| Main Authors: | , |
| 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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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862546196074070016 |
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| author | Gao, Hanpeng Schiffler, Ralf |
| author_facet | Gao, Hanpeng Schiffler, Ralf |
| citation_txt | On the Number of τ-Tilting Modules over Nakayama Algebras. Hanpeng Gao and Ralf Schiffler. SIGMA 16 (2020), 058, 13 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-17T12:03:39Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210692 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:03:39Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | On the Number of τ-Tilting Modules over Nakayama Algebras Gao, Hanpeng Schiffler, Ralf |
| title | 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_short | On the Number of τ-Tilting Modules over Nakayama Algebras |
| title_sort | on the number of τ-tilting modules over nakayama algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210692 |
| work_keys_str_mv | AT gaohanpeng onthenumberofτtiltingmodulesovernakayamaalgebras AT schifflerralf onthenumberofτtiltingmodulesovernakayamaalgebras |