Spherical subcategories in representation theory

Spherical subcategories in representation theory Math. Z. https://doi.org/10.1007/s00209-018-2075-4 Mathematische Zeitschrift 1 2 Andreas Hochenegger · Martin Kalck · David Ploog Received: 21 February 2017 / Accepted: 27 March 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardi- nality 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 Contents Introduction .................................................. 1 Spherelike objects and their spherical subcategories ........................... 1.1 Spherelike objects as derived invariants ................................ 1.2 Spherical subcategories ........................................ 2 A new triangulated invariant: the spherelike poset ............................ 3 Two quiver constructions ......................................... B Andreas Hochenegger andreas.hochenegger@unimi.it Martin Kalck m.kalck@ed.ac.uk David Ploog david.ploog@ovgu.de Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, via Cesare Saldini 50, 20133 Milan, Italy School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH93FD, Scotland, UK Institut für Algebra und Geometrie, Otto-von-Guericke Universität Magdeburg, Postfach 4120, 39016 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Spherical subcategories in representation theory

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
D.O.I.
10.1007/s00209-018-2075-4
Publisher site
See Article on Publisher Site

Abstract

Math. Z. https://doi.org/10.1007/s00209-018-2075-4 Mathematische Zeitschrift 1 2 Andreas Hochenegger · Martin Kalck · David Ploog Received: 21 February 2017 / Accepted: 27 March 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardi- nality 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 Contents Introduction .................................................. 1 Spherelike objects and their spherical subcategories ........................... 1.1 Spherelike objects as derived invariants ................................ 1.2 Spherical subcategories ........................................ 2 A new triangulated invariant: the spherelike poset ............................ 3 Two quiver constructions ......................................... B Andreas Hochenegger andreas.hochenegger@unimi.it Martin Kalck m.kalck@ed.ac.uk David Ploog david.ploog@ovgu.de Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, via Cesare Saldini 50, 20133 Milan, Italy School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH93FD, Scotland, UK Institut für Algebra und Geometrie, Otto-von-Guericke Universität Magdeburg, Postfach 4120, 39016

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jun 5, 2018

References

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