Aarhus University Seal

On higher torsion classes

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review



  • Javad Asadollahi, University of Isfahan
  • ,
  • Peter Jørgensen
  • Sibylle Schroll, University of Cologne
  • ,
  • Hipolito Treffinger, Sorbonne Université

Building on the embedding of an n-abelian category M into an abelian category A as an n-cluster-tilting subcategory of A, in this paper, we relate the n-torsion classes of M with the torsion classes of A. Indeed, we show that every n-torsion class in M is given by the intersection of a torsion class in A with M. Moreover, we show that every chain of n-torsion classes in the n-abelian category M induces a Harder–Narasimhan filtration for every object of M. We use the relation between M and A to show that every Harder–Narasimhan filtration induced by a chain of n-torsion classes in M can be induced by a chain of torsion classes in A. Furthermore, we show that n-torsion classes are preserved by Galois covering functors, thus we provide a way to systematically construct new (chains of) n-torsion classes.

Original languageEnglish
JournalNagoya Mathematical Journal
Pages (from-to)823-848
Publication statusPublished - Dec 2022

Bibliographical note

Publisher Copyright:
© (2022) The Authors.

See relations at Aarhus University Citationformats

ID: 293315558