Abstract
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.
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