If a Nakayama algebra is not cyclic, it has finite global dimension. For a cyclic Nakayama algebra, there are many characterizations of when it has finite global dimension. In [She17], Shen gave such a characterization using Ringel's resolution quiver. In [IZ92], the second author, with Zacharia, gave a cyclic homology characterization for when a monomial relation algebra has finite global dimension. We show directly that these criteria are equivalent for all Nakayama algebras. Our comparison result also reproves both characterizations. In a separate paper we discuss an interesting example that came up in our attempt to generalize this comparison result to arbitrary monomial relation algebras [HI19].

中文翻译：

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Nakayama 代数的分辨颤动和循环同源性判据

如果 Nakayama 代数不是循环的，则它具有有限的全局维度。对于循环中山代数，当它具有有限的全局维数时，有许多表征。在 [She17] 中，Shen 使用 Ringel 的分辨率箭袋给出了这样的表征。在 [IZ92] 中，第二作者和 Zacharia 给出了当单项关系代数具有有限全局维度时的循环同调表征。我们直接表明这些标准对于所有 Nakayama 代数是等价的。我们的比较结果也证实了这两种特征。在另一篇论文中，我们讨论了一个有趣的例子，我们试图将这个比较结果推广到任意的单项关系代数 [HI19]。