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An approach to non simply laced cluster algebras
Let be an oriented valued graph equipped with a group of admissible
automorphisms satisfying a certain stability condition. We prove that the
(coefficient-free) cluster algebra associated to the
valued quotient graph is a subalgebra of the quotient of the cluster algebra associated to by the action of .
When is a Dynkin diagram, we prove that and
coincide. As an example of application, we prove that
affine valued graphs are mutation-finite, giving an alternative proof to a
result of Seven.Comment: 36 pages. Minor correction
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