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.
Representation-finite tensor product algebras
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In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.
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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.