We associate a symmetric quiver with relations Q to any seed of a cluster algebra of type B and C. Under this correspondence, cluster variables of type B (resp. C) correspond to orthogonal (resp. symplectic) indecomposable representations of Q. We find a Caldero-Chapoton map in this setting. We also give a categorical interpretation of the cluster expansion formula in the case of acyclic quivers.
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Azzurra Ciliberti (2024) studied this question.
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