Generalized cluster complexes via quiver representations
Generalized cluster complexes via quiver representations
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DOI：
10.1007/s10801-007-0074-3
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发表时间：
2006-07
影响因子：
0.8
通讯作者：
Bin Zhu
中科院分区：
文献类型：
--
作者：
Bin Zhu
我们给出了 Fomin 和 Reading 定义的广义簇复合体的颤动表示理论解释。使用凯勒定义的 d 簇类别作为有价值箭袋表示的（有界）派生类别的三角轨道类别，我们在任何一对“有色”几乎正实 Schur 根上定义 ad 兼容度（−∥−），它概括了先前对非有色情况的定义，并称两个这样的根兼容，前提是它们的 d 兼容度为零。与对应于有价值的箭袋的根系统Φ相关联，利用这种相容关系，我们定义了一个单纯复形，其将几乎正的实数 Schur 根着色为顶点，将 d 兼容子集着色为单纯形。如果有价值的箭袋是 Dynkin 图的交替箭袋，那么这个复合体就是 Fomin 和 Reading 定义的广义簇复合体。
We give a quiver representation theoretic interpretation of generalized cluster complexes defined by Fomin and Reading. Usingd-cluster categories defined by Keller as triangulated orbit categories of (bounded) derived categories of representations of valued quivers, we define ad-compatibility degree (−∥−) on any pair of “colored” almost positive real Schur roots which generalizes previous definitions on the noncolored case and call two such roots compatible, provided that theird-compatibility degree is zero. Associated to the root systemΦcorresponding to the valued quiver, using this compatibility relation, we define a simplicial complex which has colored almost positive real Schur roots as vertices andd-compatible subsets as simplices. If the valued quiver is an alternating quiver of a Dynkin diagram, then this complex is the generalized cluster complex defined by Fomin and Reading.