论文标题
图片组和最大绿色序列
Picture groups and maximal green sequences
论文作者
论文摘要
我们表明，图片组与有限类型的有价值的Dynkin Quivers的最大绿色序列直接相关。也就是说，对于图片组的Coxeter元素，最大绿色序列和正表达（无逆的发电机中的单词）之间存在两者。实际上，我们证明了更通用的“垂直和水平和水平有序”集合的正面真实Schur根集（不一定是有限类型）。 此外，我们证明了这样一组积极根源的每张图片都是“原子”的线性组合，我们将原子作为特殊的半不变图片进行了精确描述。
We show that picture groups are directly related to maximal green sequences for valued Dynkin quivers of finite type. Namely, there is a bijection between maximal green sequences and positive expressions (words in the generators without inverses) for the Coxeter element of the picture group. We actually prove the theorem for the more general set up of "vertically and horizontally ordered" sets of positive real Schur roots for any hereditary algebra (not necessarily of finite type). Furthermore, we show that every picture for such a set of positive roots is a linear combination of "atoms" and we give a precise description of atoms as special semi-invariant pictures.
