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Mutating ordered $\tau$-rigid modules with applications to Nakayama algebras
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abstract
A mutation operation for $\tau$-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 $\tau$-rigid modules, which are in bijection with $\tau$-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.
Forward citations
Cited by 2 Pith papers
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Transitivity of mutation of $\tau$-exceptional sequences in the $\tau$-tilting finite case
Mutation of complete τ-exceptional sequences is transitive for every τ-tilting finite algebra.
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Mutation of $\tau$-exceptional sequences for acyclic quivers over local algebras
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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