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- Title
ON HIGHER TORSION CLASSES.
- Authors
ASADOLLAHI, JAVAD; JØRGENSEN, PETER; SCHROLL, SIBYLLE; TREFFINGER, HIPOLITO
- Abstract
Building on the embedding of an n -abelian category $\mathscr {M}$ into an abelian category $\mathcal {A}$ as an n -cluster-tilting subcategory of $\mathcal {A}$ , in this paper, we relate the n -torsion classes of $\mathscr {M}$ with the torsion classes of $\mathcal {A}$. Indeed, we show that every n -torsion class in $\mathscr {M}$ is given by the intersection of a torsion class in $\mathcal {A}$ with $\mathscr {M}$. Moreover, we show that every chain of n -torsion classes in the n -abelian category $\mathscr {M}$ induces a Harder–Narasimhan filtration for every object of $\mathscr {M}$. We use the relation between $\mathscr {M}$ and $\mathcal {A}$ to show that every Harder–Narasimhan filtration induced by a chain of n -torsion classes in $\mathscr {M}$ can be induced by a chain of torsion classes in $\mathcal {A}$. 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.
- Subjects
ABELIAN categories
- Publication
Nagoya Mathematical Journal, 2022, Vol 248, p823
- ISSN
0027-7630
- Publication type
Article
- DOI
10.1017/nmj.2022.8