Classifying Nakayama algebras with a braid group action on $\tau$-exceptional sequences

TL;DR

This paper characterizes specific Nakayama algebras where the mutation of tau-exceptional sequences aligns with braid group relations, revealing a connection to hereditary algebras or module length conditions.

Contribution

It provides a complete characterization of Nakayama algebras with braid group-compatible tau-exceptional sequence mutations, linking algebraic properties to combinatorial structures.

Findings

Mutation respects braid relations if and only if the algebra is hereditary or modules have length at least the algebra's size.

Identifies a precise criterion for braid group action compatibility in Nakayama algebras.

Connects algebraic module properties with braid group symmetries.

Abstract

We characterise those basic and connected Nakayama algebras $\Lambda$ for which the mutation of $\tau$-exceptional sequences respects the braid group relations. We show that this is the case if and only if $\Lambda$ is hereditary or all indecomposable projective $\Lambda$-modules have length at least $|\Lambda|$.