Mutation and torsion pairs

Angeleri Hügel, Lidia; Laking, Rosanna; Šťovíček, Jan; Vitória, Jorge

doi:10.2140/ant.2025.19.1313

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Mutation and torsion pairs

Lidia Angeleri Hügel, Rosanna Laking, Jan Šťovíček and Jorge Vitória

Vol. 19 (2025), No. 7, 1313–1368

DOI: 10.2140/ant.2025.19.1313

Abstract

Mutation of compact silting objects is a fundamental operation in the representation theory of finite-dimensional algebras due to its connections to cluster theory and to the lattice of torsion pairs in module or derived categories. We develop a theory of mutation in the broader framework of silting or cosilting t-structures in triangulated categories. We show that mutation of pure-injective cosilting objects encompasses the classical concept of mutation for compact silting complexes. As an application we prove that any minimal inclusion of torsion classes in the category of finitely generated modules over an artinian ring corresponds to an irreducible mutation. This generalises a well-known result for functorially finite torsion classes.

Keywords

torsion pair, t-structure, silting theory, mutation

Mathematical Subject Classification

Primary: 16E35, 16G10, 18E40, 18G80

Milestones

Received: 22 June 2023

Revised: 20 August 2024

Accepted: 23 December 2024

Published: 3 June 2025

Authors

Lidia Angeleri Hügel
Dipartimento di Informatica - Settore Matematica Università degli Studi di Verona Verona Italy

Rosanna Laking
Dipartimento di Informatica - Settore di Matematica Università degli Studi di Verona Verona Italy

Jan Šťovíček
Department of Algebra Faculty of Mathematics and Physics Charles University Praha Czech Republic

Jorge Vitória
Dipartimento di Matematica “Tullio Levi-Civita” Università degli Studi di Padova Padova Italy

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Vol. 19, No. 7, 2025