From simple-minded collections to silting objects via Koszul duality

TL;DR

This paper establishes a method to construct silting objects from simple-minded collections in derived categories of non-positive dg algebras using Koszul duality, linking two important concepts in representation theory.

Contribution

It introduces a novel construction of silting objects from simple-minded collections through Koszul duality in the context of non-positive dg algebras.

Findings

Constructs silting objects from simple-minded collections.

Utilizes Koszul duality to establish the connection.

Provides a new approach in the study of derived categories.

Abstract

Given an elementary simple-minded collection in the derived category of a non-positive dg algebra with finite-dimensional total cohomology, we construct a silting object via Koszul duality.