C‐sortable words as green mutation sequences
C‐sortable words as green mutation sequences
复制标题
C-可排序单词作为绿色突变序列
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Y. Qiu
中科院分区：
文献类型：
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作者：
Y. Qiu
设Q是一个非循环序列，s是一个顶点集Q 0中的元素序列。我们描述了有界导出范畴D（Q）中的一个简单（向后）倾斜的诱导序列，从标准心脏HQ=modkQ开始，到D（Q）中的另一个心脏Hs结束.然后我们证明了s是一个绿色突变序列当且仅当这个简单倾斜序列中的每个心脏都大于或等于HQ[−1] ;它是最大的当且仅当Hs=HQ[−1]。这提供了一种了解绿色突变的明确方法。此外，在Q的Coxeter群WQ中固定一个Coxeter元素c，它相对于Q的定向是可容许的。我们证明了由可排序字w诱导的序列w是绿色突变序列。因此，我们得到了HQ中c可排序字和有限扭类之间的双射。作为副产品，根据绿色突变的组合学给出了可分类词w的倒置、下降和覆盖反射的解释。
Let Q be an acyclic quiver and s be a sequence with elements in the vertex set Q0 . We describe an induced sequence of simple (backward) tilting in the bounded derived category D(Q) , starting from the standard heart HQ=modkQ and ending at another heart Hs in D(Q) . Then we show that s is a green mutation sequence if and only if every heart in this simple tilting sequence is greater than or equal to HQ[−1] ; it is maximal if and only if Hs=HQ[−1] . This provides a categorical way to understand green mutations. Further, fix a Coxeter element c in the Coxeter group WQ of Q , which is admissible with respect to the orientation of Q . We prove that the sequence w˜ induced by a c ‐sortable word w is a green mutation sequence. As a consequence, we obtain a bijection between c ‐sortable words and finite torsion classes in HQ . As byproducts, the interpretations of inversions, descents and cover reflections of a c ‐sortable word w are given in terms of the combinatorics of green mutations.
唐纳森-托马斯理论和簇代数
影响因子：
2.5
作者：
Nagao K
通讯作者：
Nagao K