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Mutation of {\tau}-exceptional pairs and sequences

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arxiv 2402.10301 v1 pith:AZLNNV4V submitted 2024-02-15 math.RT

Aslak B. Buan , Eric J. Hanson , Bethany R. Marsh This is my paper · ORCID
classification math.RT
keywords mutationexceptionalsequencesalgebrasmodulestransitiveadachi-iyama-reitenarbitrary
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abstract

We introduce a notion of mutation for $\tau$-exceptional sequences of modules over arbitrary finite dimensional algebras. For hereditary algebras, we show that this coincides with the classical mutation of exceptional sequences. For rank two algebras, we show that mutation of $\tau$-exceptional sequences is transitive if and only if mutation of support $\tau$-tilting modules in the sense of Adachi-Iyama-Reiten is transitive.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    math.RT 2025-06 accept novelty 7.0 of 10

    Mutation of complete τ-exceptional sequences is transitive for every τ-tilting finite algebra.

  2. Mutation of $\tau$-exceptional sequences for acyclic quivers over local algebras

    math.RT 2025-05 conditional novelty 6.0 of 10

    For algebras R⊗kQ with R local and Q acyclic, BHM mutation of complete τ-exceptional sequences coincides with classical mutation, and the braid group acts transitively.

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