Simple-minded systems and reduction for negative Calabi-Yau triangulated categories

Coelho Simões, Raquel; Pauksztello, David

doi:10.1090/tran/8002

Simple-minded systems and reduction for negative Calabi-Yau triangulated categories
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Trans. Amer. Math. Soc. 373 (2020), 2463-2498 Request permission

Abstract:

We develop the basic properties of $w$-simple-minded systems in $(-w)$-Calabi-Yau triangulated categories for $w \geqslant 1$. We show that the theory of simple-minded systems exhibits striking parallels with that of cluster-tilting objects. The main result is a reduction technique for negative Calabi-Yau triangulated categories. Our construction provides an inductive technique for constructing simple-minded systems.

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