布拉耶尔图代数在Morita型稳定等价下的分类
Classification of Brauer graph algebras under stable equivalence of Morita type
AI总结：
本文证明布拉耶尔图代数的导出等价与Morita型稳定等价等价，并将此结论应用于稳定Picard群轨道的研究，同时给出该类代数在Morita型稳定等价下对半单直和项封闭的新证明。
AI中文摘要：
Opper与Zvonareva近期给出了导出等价下布拉耶尔图代数的分类。本文证明，两个布拉耶尔图代数导出等价当且仅当它们是Morita型稳定等价的。作为应用，我们证明Morita型简单像的每个稳定Picard群轨道都包含一个可提升的代表元。此外，我们给出了一个新的证明：布拉耶尔图代数在Morita型稳定等价下对半单直和项是封闭的。
英文摘要：
The classification of Brauer graph algebras under derived equivalence was recently given by Opper and Zvonareva. In this paper, we prove that two Brauer graph algebras are derived equivalent if and only if they are stably equivalent of Morita type. As an application, we show that every stable Picard group orbit of simple-images of Morita type contains a liftable representative. Moreover, we give a new proof of the fact that Brauer graph algebras are closed up to semisimple summands under stable equivalence of Morita type.
