On the Number of $\tau$-Tilting Modules over Nakayama Algebras

Symmetry Integrability and Geometry-Methods and Applications

article

Hanpeng Gao¹  Ralf Schiffler² 

[1] Department of Mathematics, Nanjing University;Department of Mathematics, University of Connecticut

关键词: τ -tilting modules;    support τ -tilting modules;    Nakayama algebras;   

DOI  :  10.3842/SIGMA.2020.058

来源: National Academy of Science of Ukraine

【 摘 要 】

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 $\widetilde{\Lambda}^r_n$.

【 授权许可】

Unknown