Derived categories of graded gentle one-cycle algebras

TL;DR

This paper explores the structure of derived categories of graded gentle one-cycle algebras, showing they can be understood as triangulated hulls of orbit categories, advancing the understanding of their homological properties.

Contribution

It introduces a new perspective by relating derived categories of graded gentle one-cycle algebras to orbit categories, providing a novel framework for their analysis.

Findings

Derived categories are triangulated hulls of orbit categories.

Application to graded gentle one-cycle algebras.

Enhanced understanding of their homological structure.

Abstract

Let $A$ be a graded algebra. It is shown that the derived category of dg modules over $A$ (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded $A$-modules. This is applied to study derived categories of graded gentle one-cycle algebras.