Subquivers of mutation-acyclic quivers are mutation-acyclic

Details Subquivers of mutation-acyclic quivers are mutation-acyclic Subquivers of mutation-acyclic quivers are mutation-acyclic

2011-02-16

arxiv.org/abs/1102.3382v2

Mathematics

Representation Theory

v2: main result was found to be already known, introduction changed correspondingly

Scientific paper

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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