Background
Type: Article

ON HIGHER TORSION CLASSES

Journal: Nagoya Mathematical Journal (00277630)Year: 2022/12/10Volume: 248Issue: Pages: 823 - 848
Asadollahi J.a Jørgensen P. Schroll S. Treffinger H.
Green • Hybrid GoldDOI:10.1017/nmj.2022.8Language: English

Abstract

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. © (2022) The Authors.


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