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

Coelho Simoes, Raquel and Pauksztello, David (2020) Simple-minded systems and reduction for negative Calabi-Yau triangulated categories. Transactions of the American Mathematical Society, 373 (4). pp. 2463-2498. ISSN 0002-9947

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Abstract

We develop the basic properties of w-simple-minded systems in (-w)-Calabi-Yau triangulated categories for w≥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.