Derived equivalences between subrings

TL;DR

This paper develops a method to construct derived equivalences between subrings of endomorphism rings in abelian categories, based on short exact sequences, generalizing existing approaches.

Contribution

It introduces a new approach to derive equivalences between subrings of endomorphism rings from arbitrary short exact sequences in abelian categories.

Findings

Constructed derived equivalences from short exact sequences.

Generalized existing methods for deriving equivalences.

Applicable to subrings of $ ext{End}$ rings in abelian categories.

Abstract

In this paper, we construct derived equivalences between two subrings of relevant $\Phi$-Auslander-Yoneda rings from an arbitrary short exact sequence in an abelian category. As a consequence, any short exact sequence in an abelian category gives rise to a derived equivalence between two subrings of endomorphism rings. These results generalize some methods on constructing derived equivalences.