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Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 113–147 | Cite as

Spherical subcategories in representation theory

  • Andreas HocheneggerEmail author
  • Martin Kalck
  • David Ploog
Article

Abstract

We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality and the height of the poset. We explicitly describe spherical subcategories and their poset structure for derived categories of certain finite-dimensional algebras.

Keywords

Spherical object Spherelike object Spherical subcategory Spherelike poset Derived invariant Cluster-tilting Finite-dimensional algebra Quiver 

Mathematics Subject Classification

16E35 16G20 18E30 

Notes

Acknowledgements

We are grateful to Gustavo Jasso and Yanki Lekili for discussion and comments. Moreover, we thank Matthew Pressland for suggesting how to generalise Lemma 3.27 to Remark 3.29. Finally we want to thank the anonymous referees for valuable comments. Martin Kalck is grateful for the support by DFG Grant Bu-1886/2-1 and EPSRC Grant EP/L017962/1.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Andreas Hochenegger
    • 1
    Email author
  • Martin Kalck
    • 2
  • David Ploog
    • 3
  1. 1.Dipartimento di Matematica “Federigo Enriques”Università degli Studi di MilanoMilanItaly
  2. 2.School of MathematicsUniversity of EdinburghEdinburghUK
  3. 3.Institut für Algebra und GeometrieOtto-von-Guericke Universität MagdeburgMagdeburgDeutschland

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