ON HIGHER TORSION CLASSES

ASADOLLAHI, JAVAD; JØRGENSEN, PETER; SCHROLL, SIBYLLE; TREFFINGER, HIPOLITO

NAGOYA MATHEMATICAL JOURNAL

NAGOYA UNIV

Año: 2022 vol. 248 p. 823 - 848

0027-7630

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.