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Algebras and Representation Theory

, Volume 17, Issue 2, pp 565–591 | Cite as

Torsion Pairs and Rigid Objects in Tubes

  • Karin Baur
  • Aslak Bakke Buan
  • Robert J. MarshEmail author
Article

Abstract

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Prüfer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs, maximal rigid objects and the bijection between them geometrically. We also give a similar geometric description in the case of the linear orientation of a Dynkin quiver of type A.

Keywords

Tube category Torsion pair Torsion theory Pruefer module Adic module Annulus Maximal rigid object Arc model Direct limit Inverse limit 

Mathematics Subject Classifications (2010)

Primary 16G10 16G70 55N45; Secondary 13F60 16G20 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Karin Baur
    • 1
  • Aslak Bakke Buan
    • 2
  • Robert J. Marsh
    • 3
    Email author
  1. 1.Institut für Mathematik und wissenschaftliches RechnenUniversität GrazGrazAustria
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  3. 3.School of MathematicsUniversity of LeedsLeedsEngland

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