Derived Picard Groups of Preprojective Algebras of Dynkin Type
Derived Picard Groups of Preprojective Algebras of Dynkin Type
复制标题
Dynkin型原投影代数的派生Picard群
DOI：
10.1093/imrn/rny299
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发表时间：
2019
影响因子：
1
通讯作者：
Mizuno Yuya
中科院分区：
文献类型：
--
作者：
Mizuno Yuya
本文研究了Dynkin型预投影代数的双面倾斜复形。我们构造了最基本的一类双面倾斜配合物，它具有由派生张量积构成的群结构，并推导出派生范畴的一组自等价。证明了双面倾斜配合物的群结构与相应折叠图的编织群是同构的。此外，我们还证明了这些双边倾斜配合物会引起倾斜突变，并给出了任何倾斜配合物的导数张量积。利用这些结果，我们确定了类型和的预投影代数的派生Picard群。
In this paper, we study two-sided tilting complexes of preprojective algebras of Dynkin type. We construct the most fundamental class of two-sided tilting complexes, which has a group structure by derived tensor products and induces a group of auto-equivalences of the derived category. We show that the group structure of the two-sided tilting complexes is isomorphic to the braid group of the corresponding folded graph. Moreover, we show that these two-sided tilting complexes induce tilting mutation and any tilting complex is given as the derived tensor products of them. Using these results, we determine the derived Picard group of preprojective algebras for typeand.