A categorification of cluster algebras of type B and C through symmetric quivers
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910033926684672 |
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| author | Ciliberti, Azzurra |
| author_facet | Ciliberti, Azzurra |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11308 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A categorification of cluster algebras of type B and C through symmetric quivers Ciliberti, Azzurra Representation Theory Combinatorics 13F60, 16G20 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. |
| title | A categorification of cluster algebras of type B and C through symmetric quivers |
| topic | Representation Theory Combinatorics 13F60, 16G20 |
| url | https://arxiv.org/abs/2403.11308 |