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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2020
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210692 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
|
|---|---|
| ISSN: | 1815-0659 |