Let A be a representation-finite self-injective algebra over an algebraically closed field k. We give a new characterization for an orthogonal system in the stable module category A-\(\underline {\text {mod}}\) to be a simple-minded system. As a by-product, we show that every Nakayama-stable orthogonal system in A-\(\underline {\text {mod}}\) extends to a simple-minded system.

中文翻译：

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表示有限自射代数上简单思想的系统

设A是代数封闭场k上的表示有限的自内射代数。我们在稳定模块类别A - \（\下划线{\ text {mod}} \\）中将正交系统作为一个简单的系统进行了新的描述。作为副产品，我们证明A - \（\下划线{\ text {mod}} \\）中的每个中山稳定正交系统都扩展到一个简单的系统。