Derived equivalences in n-angulated categories

TL;DR

This paper explores how $n$-angles in $n$-angulated categories induce derived equivalences between quotient algebras of $n$-perforated Yoneda algebras, linking higher cluster theory with derived equivalences.

Contribution

It generalizes existing results by showing $n$-angles induce derived equivalences, connecting higher cluster theory and derived categories in a novel way.

Findings

$n$-angles induce derived equivalences between quotient algebras

Establishes a connection between higher cluster theory and derived equivalences

Generalizes previous results by Hu, K"{o}nig, and Xi

Abstract

In this paper, we consider $n$-perforated Yoneda algebras for $n$-angulated categories, and show that, under some conditions, $n$-angles induce derived equivalences between the quotient algebras of $n$-perforated Yoneda algebras. This result generalizes some results of Hu, K\"{o}nig and Xi. And it also establishes a connection between higher cluster theory and derived equivalences. Namely, in a cluster tilting subcategory of a triangulated category, an Auslander-Reiten $n$-angle implies a derived equivalence between two quotient algebras. This result can be compared with the fact that an Auslander-Reiten sequence suggests a derived equivalence between two algebras which was proved by Hu and Xi.