On silting theory for complete path algebras

Abstract

Let $Q$ be a finite quiver and let $Λ$ be the complete path algebra of $Q$ with respect to the arrow ideal. We study the mutation of silting objects in the bounded homotopy category of projective $Λ$-modules and characterise in which cases the mutation theories of silting complexes and 2-term silting complexes of $Λ$ are determined by those of a finite dimensional quotient $Λ/I$. This characterisation is closely related to a characterisation of 2-term silting finite quotient algebras.