Transfer of derived equivalences from subalgebras to endomorphism algebras II

TL;DR

This paper explores how derived equivalences between certain subalgebras in weakly n-angulated categories can be transferred to endomorphism algebras, extending previous work to n-angle cases with explicit examples.

Contribution

It extends the transfer of derived equivalences from subalgebras to endomorphism algebras to the setting of n-angles in weakly n-angulated categories, generalizing prior results.

Findings

Established a method to transfer derived equivalences via n-angles.

Extended previous constructions to n-angle cases.

Provided an explicit example illustrating the theoretical results.

Abstract

We investigate derived equivalences between subalgebras of some $\Phi$-Auslander-Yoneda algebras from a class of $n$-angles in weakly $n$-angulated categories. The derived equivalences are obtained by transferring subalgebras induced by $n$-angles to endomorphism algebras induced by approximation sequences. Then we extend our constructions \cite{BP} to $n$-angle cases. Finally, we give an explicit example to illustrate our result.