论文标题
关于$τ$的数量 - nakayama代数的模块
On the Number of $τ$-Tilting Modules over Nakayama Algebras
论文作者
论文摘要
让$λ^r_n $为$ \ mathbb {a} $线性定向颤动的路径代数，带有$ n $ vertices modulo $ r $ - $ r $ - $ \ \ \ \ \ \wideTildeλ^r_n $是周期性的$ wideted $ widete $ \ quiverbra a i^用$ n $顶点modulo，$ r $ $ th的功率。 Adachi给出了$τ$的$λ^r_n $的$τ$的重复关系。在本文中，我们表明，相同的复发关系也适用于$ \ \ \ \ \widetildeλ^r_n $的$τ$的数量。作为一个应用程序，我们为Asai在复发公式中提供了新的证明，以$λ^r_n $和$ \widetildeλ^r_n $的支持$τ$的数量。
Let $Λ^r_n$ 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 $\widetildeΛ^r_n$ 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 $τ$-tilting modules over $Λ^r_n$. In this paper, we show that the same recurrence relation also holds for the number of $τ$-tilting modules over $\widetildeΛ^r_n$. 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 $Λ^r_n$ and $\widetildeΛ^r_n$.
