Derived preprojective algebras and spherical twist functors

TL;DR

This paper explores the relationship between silting objects, spherical twist functors, and mutations in derived preprojective algebras of acyclic quivers, establishing a bijection with the braid group for Dynkin quivers.

Contribution

It introduces a direct relationship between silting objects, spherical twist functors, and mutations, and establishes a bijection between braid group elements and silting objects for Dynkin quivers.

Findings

Bijection between braid group elements and silting objects for Dynkin quivers

Relationship established between silting objects, spherical twists, and mutations

Enhanced understanding of derived preprojective algebras of acyclic quivers

Abstract

We study silting objects over derived preprojective algebras of acyclic quivers by giving a direct relationship between silting objects, spherical twist functors and mutations. Especially, for a Dynkin quiver, we establish a bijection between the elements of the braid group and the set of isomorphism classes of basic silting objects over the derived preprojective algebra.