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This article is cited in 2 scientific papers (total in 2 papers)
On the Number of $\tau$-Tilting Modules over Nakayama Algebras
Hanpeng Gaoa, Ralf Schifflerb a Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China
b Department of Mathematics, University of Connecticut, Storrs, CT 06269-1009, USA
Abstract:
Let $\Lambda^r_n$ be the path algebra of the linearly oriented quiver of type $\mathbb{A}$ with $n$ vertices modulo the $r$-th power of the radical, and let $\widetilde{\Lambda}^r_n$ be the path algebra of the cyclically oriented quiver of type $\widetilde{\mathbb{A}}$ with $n$ vertices modulo the $r$-th power of the radical. Adachi gave a recurrence relation for the number of $\tau$-tilting modules over $\Lambda^r_n$. In this paper, we show that the same recurrence relation also holds for the number of $\tau$-tilting modules over $\widetilde{\Lambda}^r_n$. As an application, we give a new proof for a result by Asai on recurrence formulae for the number of support $\tau$-tilting modules over $\Lambda^r_n$ and $\widetilde{\Lambda}^r_n$.
Keywords:
$\tau$-tilting modules, support $\tau$-tilting modules, Nakayama algebras.
Received: March 6, 2020; in final form June 11, 2020; Published online June 18, 2020
Citation:
Hanpeng Gao, Ralf Schiffler, “On the Number of $\tau$-Tilting Modules over Nakayama Algebras”, SIGMA, 16 (2020), 058, 13 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1595 https://www.mathnet.ru/eng/sigma/v16/p58
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