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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Simple-minded systems and reduction for negative Calabi-Yau triangulated categories
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by Raquel Coelho Simões and David Pauksztello PDF
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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Additional Information
  • 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
  • Email: rcoelhosimoes@campus.ul.pt
  • David Pauksztello
  • Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, United Kingdom
  • MR Author ID: 833009
  • Email: d.pauksztello@lancaster.ac.uk
  • 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.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 2463-2498
  • MSC (2010): Primary 18E30, 16G10
  • DOI: https://doi.org/10.1090/tran/8002
  • MathSciNet review: 4069225