On reduction and gluing technique of simple-minded systems over self-injective algebras

Let A be a self-injective algebra over an algebraically closed field. We study reduction of simple-minded systems over the stable module category A-mod―. We present a recollement and study gluing technique of simple-minded systems through a subset of a simple-minded system in A-mod―. As a byproduct, we also study the extendible property of simple-minded systems.