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Transactions of the American Mathematical Society

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

Authors: Raquel Coelho Simões and David Pauksztello
Journal: Trans. Amer. Math. Soc. 373 (2020), 2463-2498
MSC (2010): Primary 18E30, 16G10
Published electronically: January 7, 2020
MathSciNet review: 4069225
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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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Raquel Coelho Simões
Affiliation: Centro de Análise Funcional, Estruturas Lineares e Aplicações, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Edifício C6, Piso 2, 1749-016, Lisboa, Portugal

David Pauksztello
Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, United Kingdom
MR Author ID: 833009

Keywords: Simple-minded system, simple-minded mutation pair, Calabi-Yau triangulated category, Calabi-Yau reduction
Received by editor(s): September 13, 2018
Received by editor(s) in revised form: July 19, 2019
Published electronically: January 7, 2020
Additional Notes: The first author was supported by Fundação para a Ciência e Tecnologia through Grant SFRH/BPD/90538/2012 and Project UID/MAT/04721/2013.
Article copyright: © Copyright 2019 American Mathematical Society