Transitivity of mutation of $\tau$-exceptional sequences in the $\tau$-tilting finite case

TL;DR

This paper proves that in the context of $ au$-tilting finite algebras, the mutation process of complete $ au$-exceptional sequences is transitive, establishing a fundamental property of their structure.

Contribution

It demonstrates the transitivity of mutation for complete $ au$-exceptional sequences specifically in $ au$-tilting finite algebras, a property not previously established.

Findings

Mutation of complete $ au$-exceptional sequences is transitive in $ au$-tilting finite algebras.

Provides a foundational result for the structure theory of $ au$-tilting finite algebras.

Enhances understanding of mutation dynamics in $ au$-tilting theory.

Abstract

We prove that mutation of complete $\tau$-exceptional sequences is transitive for $\tau$-tilting finite algebras.