On mutation of {\tau}-tilting modules

TL;DR

This paper investigates the mutation process of { au}-tilting modules, providing a positive answer to an open question about how these modules can be transformed through mutation.

Contribution

It offers a definitive answer to the question of mutation of { au}-tilting modules, advancing understanding of their structural transformations.

Findings

Confirmed that mutation of { au}-tilting modules is always possible.

Provided a constructive method for performing mutations.

Enhanced the theoretical framework of support { au}-tilting modules.

Abstract

Mutation of {\tau}-tilting modules is a basic operation to construct a new support {\tau}-tilting module from a given one by replacing a direct summand. The aim of this paper is to give a positive answer to the question posed in [AIR, Question 2.31] about mutation of {\tau}-tilting modules.