d-Representation-finite self-injective algebras
d-Representation-finite self-injective algebras
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DOI：
10.1016/j.aim.2019.106932
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发表时间：
2017-02
影响因子：
1.7
通讯作者：
Erik Darpo;O. Iyama
中科院分区：
文献类型：
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作者：
Erik Darpo;O. Iyama
本文主要研究自内射代数的高维Auslander-Reiten理论。我们给出了一个系统的结构（弱）d-表示有限自内射代数作为轨道代数的重复范畴的有限的整体维数满足一定的有限性条件的Serre函子。这个条件特别适用于所有至多为全局维数的分数阶Calabi-Yau代数。这推广了Riedtmann关于表示有限自内射代数的经典构造。我们的方法是基于适应加布里埃尔的覆盖理论叉线性类别设置的高维Auslander-Reiten theory.Applications includen-fold平凡extensions和（古典和更高）预投射代数，这是床表示有限的在许多情况下。我们还得到了任意d的全d表示有限自内射Nakayama代数的一个完全分类。
In this paper, we initiate the study of higher-dimensional Auslander–Reiten theory of self-injective algebras. We give a systematic construction of (weakly)d-representation-finite self-injective algebras as orbit algebras of the repetitive categories of algebras of finite global dimension satisfying a certain finiteness condition for the Serre functor. The condition holds, in particular, for all fractionally Calabi-Yau algebras of global dimension at mostd. This generalizes Riedtmann's classical construction of representation-finite self-injective algebras. Our method is based on an adaptation of Gabriel's covering theory fork-linear categories to the setting of higher-dimensional Auslander–Reiten theory.Applications includen-fold trivial extensions and (classical and higher) preprojective algebras, which are shown to bed-representation-finite in many cases. We also get a complete classification of alld-representation-finite self-injective Nakayama algebras for arbitraryd.