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

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/04/2020
<mark>Journal</mark>Transactions of the American Mathematical Society
Issue number4
Volume373
Number of pages36
Pages (from-to)2463-2498
Publication statusPublished
Early online date7/01/20
Original languageEnglish

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.