Mutation of torsion pairs of small modules and silting subcategories
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The goal of the representation theory of algebras is to study the richness of the abstract algebraic structures known as “algebras” via their “modules” (or “representations”), each of which partially models the structure of the algebra. Torsion pairs of small modules over an algebra allow one to decompose its category of small modules into a pair of simpler “disjointed” subcategories from which the entire category can then be reconstructed. Since each torsion pair provides a unique decomposition, being able to control them yields a powerful tool for the study of this category. In this talk, we give a brief overview of the theory for mutation of torsion pairs of small modules, with a particular focus on their relation to silting subcategories—including “large” (i.e. either product or coproduct-closed) silting subcategories, which we note can be used to mutate bounded (co)silting complexes. Links: TBD.