ON HIGHER TORSION CLASSES - Kölner UniversitätsPublikationsServer

Asadollahi, Javad, Jorgensen, Peter, Schroll, Sibylle ORCID: 0000-0001-9618-7647 and Treffinger, Hipolito (2022). ON HIGHER TORSION CLASSES. Nagoya Math. J., 248. S. 823 - 849. NEW YORK: CAMBRIDGE UNIV PRESS. ISSN 2152-6842

Full text not available from this repository.

DOI:10.1017/nmj.2022.8

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.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Asadollahi, Javad	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Jorgensen, Peter	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Schroll, Sibylle	UNSPECIFIED	orcid.org/0000-0001-9618-7647	UNSPECIFIED
Treffinger, Hipolito	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED