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arXiv · 1102.3382

Subquivers of mutation-acyclic quivers are mutation-acyclic

Matthias Warkentin
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Abstract

Quiver mutation plays a crucial role in the definition of cluster algebras by Fomin and Zelevinsky. It induces an equivalence relation on the set of all quivers without loops and two-cycles. A quiver is called mutation-acyclic if it is mutation-equivalent to an acyclic quiver. This note gives a proof that full subquivers of mutation-acyclic quivers are mutation-acyclic.

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Matthias Warkentin. 2011-02-16. Subquivers of mutation-acyclic quivers are mutation-acyclic. https://arxiv.org/abs/1102.3382

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