论文标题
$ c $ - 向量和有限类型无环砂的非自身横断曲线
$C$-Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type
论文作者
论文摘要
让$ Q $是无环箭弹，$ k $是代数关闭的字段。对路径代数$ kq $的不可分解的异常模块进行了广泛的研究。与$ Q $相关的根系的真正Schur根是不可分解的异常模块的维度向量。它已在[NájeraChávezA。，int。数学。 res。不是。 2015年（2015年），1590-1600]，对于无环砂，一组积极的$ c $ - 向量和一组真正的Schur Roots是一致的。给出$ C $ - 向量的图解描述，K-H。 Lee和K. Lee猜想，对于无环砂，$ c $ - 向量的集合和对应于非自动交叉的可允许曲线的根组等于集合[Exp。数学，出现，Arxiv：1703.09113]。在[adv。数学。 340（2018），855-882]，A。Felikson和P. tumarkin证明了这一猜想的2杯砂。在本文中，我们证明了针对$ a $ a $，$ d $和$ e_ {6} $和$ e_7 $的李 - 李猜想的修订版。
Let $Q$ be an acyclic quiver and $k$ be an algebraically closed field. The indecomposable exceptional modules of the path algebra $kQ$ have been widely studied. The real Schur roots of the root system associated to $Q$ are the dimension vectors of the indecomposable exceptional modules. It has been shown in [Nájera Chávez A., Int. Math. Res. Not. 2015 (2015), 1590-1600] that for acyclic quivers, the set of positive $c$-vectors and the set of real Schur roots coincide. To give a diagrammatic description of $c$-vectors, K-H. Lee and K. Lee conjectured that for acyclic quivers, the set of $c$-vectors and the set of roots corresponding to non-self-crossing admissible curves are equivalent as sets [Exp. Math., to appear, arXiv:1703.09113]. In [Adv. Math. 340 (2018), 855-882], A. Felikson and P. Tumarkin proved this conjecture for 2-complete quivers. In this paper, we prove a revised version of Lee-Lee conjecture for acyclic quivers of type $A$, $D$, and $E_{6}$ and $E_7$.
