τ2-Stable tilting complexes over weighted projective lines
τ2-Stable tilting complexes over weighted projective lines
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DOI：
10.1016/j.aim.2014.12.018
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发表时间：
2014-02
影响因子：
1.7
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文献类型：
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令 X 为加权投影线，coh X 为相干滑轮的相关类别。我们对 D b (coh X) 中的倾斜复合体 T 进行分类，使得 τ 2 T≅ T，其中 τ 是 D b (coh X) 中的 Auslander-Reiten 平移。作为该结果的应用，我们对导出等价于规范代数的 2 表示有限代数进行分类。这补充了 Iyama-Oppermann 迭代倾斜 2 表示有限代数的分类。通过传递到3-预射代数，我们获得了规范型自射簇倾斜代数的分类。这补充了林格尔对自射簇倾斜代数的分类。
Let X be a weighted projective line and coh X the associated category of coherent sheaves. We classify the tilting complexes T in D b (coh X) such that τ 2 T≅ T, where τ is the Auslander–Reiten translation in D b (coh X). As an application of this result, we classify the 2-representation-finite algebras which are derived-equivalent to a canonical algebra. This complements Iyama–Oppermann's classification of the iterated tilted 2-representation-finite algebras. By passing to 3-preprojective algebras, we obtain a classification of the selfinjective cluster-tilted algebras of canonical-type. This complements Ringel's classification of the selfinjective cluster-tilted algebras.