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

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<mark>Journal publication date</mark>8/09/2019
<mark>Journal</mark>Transactions of the American Mathematical Society
Number of pages36
Publication statusAccepted/In press
Original languageEnglish

Abstract

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