تقرير
A categorification of cluster algebras of type B and C through symmetric quivers
| العنوان: | A categorification of cluster algebras of type B and C through symmetric quivers |
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| المؤلفون: | Ciliberti, Azzurra |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Combinatorics |
| الوصف: | 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. Comment: 38 pages. v2: minor changes |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.11308 |
| رقم الأكسشن: | edsarx.2403.11308 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |