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Mutating ordered $τ$-rigid modules with applications to Nakayama algebras

Year: 2025

Type: preprint

Abstract: A mutation operation for $τ$-exceptional sequences of modules over any finite-dimensional algebra was recently introduced, generalising the mutation for exceptional sequences of modules over hereditary algebras. We interpret this mutation in terms of TF-ordered $τ$-rigid modules, which are in bijection with $τ$-exceptional sequences. As an application we show that the mutation is transitive for Nakayama algebras, by providing an explicit combinatorial description of mutation over this class of algebras.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2501.13694

Authors: Buan, Aslak B., Kaipel, Maximilian, Terland, Håvard U.

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4406793424

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