论文标题
镜像反射代数和Tachikawa的第二个猜想
Mirror-reflective algebras and Tachikawa's second conjecture
论文作者
论文摘要
鉴于一个具有同性恋的代数，我们介绍了两个程序，以构建新代数的家族，称为镜面反射代数和减少的镜面反射代数。然后，我们通过对派生模块类别的回忆来建立这些代数之间的连接。如果给定代数为gendo对称，我们表明（降低的）镜像反射代数是对称的，并提供了新的方法来系统地构建高维（最小）Auslander-Gorenstein代数和Gendo-Arge-Memertim-Metres-Metres-Metres-Metres-Metres-Metres-Metightric代数。这导致了Tachikawa在基本代数的第二个猜想中的新表述。
Given an algebra with an idempotent, we introduce two procedures to construct families of new algebras, termed mirror-reflective algebras and reduced mirror-reflective algebras. We then establish connections among these algebras by recollements of derived module categories. In case of given algebras being gendo-symmetric, we show that the (reduced) mirror-reflective algebras are symmetric and provide new methods to construct systematically both higher dimensional (minimal) Auslander-Gorenstein algebras and gendo-symmetric algebras of higher dominant dimensions. This leads to a new formulation of Tachikawa's second conjecture for symmetric algebras in terms of idempotent stratifications.
