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Mutation and Torsion Pairs by Hügel, Lidia Angeleri; Laking, Rosanna; Šťovíček, Jan; Vitória, Jorge is a scholarly article available to read on EtoBox.

What is Mutation and Torsion Pairs about?

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. In this paper 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.

Author

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

Published

2022

Language

EN