On derived equivalences of Nakayama algebras

TL;DR

This paper introduces a method to establish derived equivalences between specific Nakayama algebras using the concept of S-families within triangulated categories.

Contribution

It presents a novel approach leveraging S-families to construct derived equivalences for Nakayama algebras, expanding the understanding of their categorical relationships.

Findings

Established new derived equivalences between Nakayama algebras.

Developed the concept of S-families in the context of triangulated categories.

Provided a framework for future research on algebraic equivalences.

Abstract

In this paper, we construct derived equivalences between certain Nakayama algebras by using the notion of an S-family which is a family of objects in a triangulated category satisfying some axioms.