Stability Conditions and Maximal Green Sequences in Abelian Categories

TL;DR

This paper explores stability functions in abelian categories, their connection to torsion classes and maximal green sequences, and introduces a new stability function compatible with wall and chamber structures.

Contribution

It introduces a novel stability function compatible with wall and chamber structures and analyzes their relation to torsion classes and maximal green sequences in abelian categories.

Findings

Established a new stability function compatible with wall and chamber structures.

Linked stability functions with torsion classes and maximal green sequences.

Provided theoretical insights into the structure of abelian categories.

Abstract

In this paper we study the stability functions on abelian categories introduced by Rudakov in \cite{Ru} and their relation with torsion classes and maximal green sequences. Moreover we introduce a new kind of stability function which is compatible with the wall and chamber of the category.