A categorification of cluster algebras of type B and C through symmetric quivers
Abstract
We express cluster variables of type Bn and Cn in terms of cluster variables of type An. Then we associate a cluster tilted bound symmetric quiver Q of type A2n-1 to any seed of a cluster algebra of type Bn and Cn. Under this correspondence, cluster variables of type Bn (resp. Cn) 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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