Balanced pairs and tilting modules in recollement

TL;DR

This paper explores the relationships of balanced pairs and introduces relative tilting modules within Abelian categories in a recollement, providing new characterizations and examining their interrelations.

Contribution

It introduces the concept of relative tilting modules in recollements and characterizes them similarly to Bazzoni's n-tilting modules, advancing the understanding of their structure.

Findings

Characterization of relative tilting modules in recollements

Relationship between balanced pairs in Abelian categories

Application of admissible balanced pairs

Abstract

In this paper, firstly, we mainly study the relationship of balanced pairs among three Abelian categories in a recollement. As an application of admissible balanced pairs, we introduce the notion of the relative tilting modules, and give a characterization of relative tilting modules, which similar to Bazzoni characterization of n-tilting modules [4]. Finally, we mainly consider the relationship of relative tilting modules in a recollement.