论文标题
正交模块的同源理论
Homological theory of orthogonal modules
论文作者
论文摘要
Tachikawa的第二个猜想预测，有限生成的正交模块在有限维自注射的代数上是投影。这个猜想是中山猜想的重要组成部分。我们对这项工作的主要动机是从稳定模块类别的角度对有限生成的正交发电机的系统理解。结果，对于正交发电机M，我们建立了对M相关稳定类别的回忆，描述回忆的正确项的紧凑对象，并在M-Gorenstein类别中对Tachikawa的第二个猜想进行了同等的特征。此外，我们介绍了Gorenstein-Morita代数，并表明Nakayama的猜想对他们来说是正确的。
Tachikawa's second conjecture predicts that a finitely generated, orthogonal module over a finite-dimensional self-injective algebra is projective. This conjecture is an important part of the Nakayama conjecture. Our principal motivation of this work is a systematic understanding of finitely generated, orthogonal generators over a self-injective Artin algebra from the view point of stable module categories. As a result, for an orthogonal generator M, we establish a recollement of the M-relative stable categories, describe compact objects of the right term of the recollement, and give equivalent characterizations of Tachikawa's second conjecture in terms of M-Gorenstein categories. Further, we introduce Gorenstein-Morita algebras and show that the Nakayama conjecture holds true for them.
