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arXiv · 2403.11308

A categorification of cluster algebras of type B and C through symmetric quivers

Azzurra Ciliberti
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Abstract

We express cluster variables of type $B_n$ and $C_n$ in terms of cluster variables of type $A_n$. Then we associate a cluster tilted bound symmetric quiver $Q$ of type $A_{2n-1}$ to any seed of a cluster algebra of type $B_n$ and $C_n$. Under this correspondence, cluster variables of type $B_n$ (resp. $C_n$) 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. 2024-03-17. A categorification of cluster algebras of type B and C through symmetric quivers. https://doi.org/10.1016/j.jalgebra.2024.09.015

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