Full exceptional collections and stability conditions for Dynkin quivers

TL;DR

This paper proves that for any stability condition on the derived category of a Dynkin quiver, there exists a full sigma-exceptional collection, advancing the understanding of stability conditions in derived categories.

Contribution

It establishes the existence of full sigma-exceptional collections for all stability conditions on derived categories of Dynkin quivers, a new result in the field.

Findings

Every stability condition on a Dynkin quiver's derived category admits a full sigma-exceptional collection.

The work extends the understanding of the structure of stability conditions in derived categories.

Provides a foundation for further exploration of derived categories and stability conditions in representation theory.

Abstract

For a stability condition $\sigma$ on a triangulated category, Dimitrov-Katzarkov introduced the notion of a $\sigma$-exceptional collection. In this paper, we study full $\sigma$-exceptional collections in the derived category of an acyclic quiver. In particular, we prove that any stability condition $\sigma$ on the derived category of a Dynkin quiver admits a full $\sigma$-exceptional collection.