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On Auslander–Reiten translates in functorially finite subcategories and applications

Volume 119 / 2010

K. Erdmann, D. Madsen, V. Miemietz Colloquium Mathematicum 119 (2010), 51-77 MSC: 16G70, 18G25, 20G05, 17B10. DOI: 10.4064/cm119-1-3

Abstract

We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander–Reiten sequences. We also prove an Auslander–Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when this category has finite type. The class of these algebras contains all blocks of Schur algebras $S(2,r)$.

Authors

  • K. ErdmannMathematical Institute
    University of Oxford
    24-29 St Giles'
    OX1 3LB, Oxford, UK
    e-mail
  • D. MadsenMathematics Department
    215 Carnegie
    Syracuse University
    Syracuse, NY 13244, U.S.A.
    e-mail
  • V. MiemietzMathematical Institute
    University of Oxford
    24-29 St Giles'
    OX1 3LB, Oxford, UK
    e-mail

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