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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210692 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the Number of τ-Tilting Modules over Nakayama Algebras. Hanpeng Gao and Ralf Schiffler. SIGMA 16 (2020), 058, 13 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 |