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Simple-minded systems and reduction for negative Calabi-Yau triangulated categories (1808.02519v1)
Published 7 Aug 2018 in math.RT
Abstract: We develop the basic properties of $w$-simple-minded systems in $(-w)$-Calabi-Yau triangulated categories for $w \geq 1$. The main result is a reduction technique for negative Calabi-Yau triangulated categories. We show that the theory of simple-minded systems exhibits striking parallels with that of cluster-tilting objects. Our construction provides an inductive technique for constructing simple-minded systems.