A multiplication formula for cluster characters in gentle algebras
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911141984206848 |
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| author | Ciliberti, Azzurra |
| author_facet | Ciliberti, Azzurra |
| contents | We prove a multiplication formula for cluster characters induced by generating extensions in a gentle algebra A, generalizing a result of Cerulli Irelli, Esposito, Franzen, Reineke. In the case where A is the gentle algebra of a triangulation T of an unpunctured marked surface, this provides a representation-theoretic interpretation of the exchange relations in the cluster algebra with principal coefficients in T. As an application, we interpret a formula that relates cluster variables of type B to cluster variables of type A in the symmetric module category of the algebras arising from special triangulations of a regular polygon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A multiplication formula for cluster characters in gentle algebras Ciliberti, Azzurra Representation Theory Rings and Algebras We prove a multiplication formula for cluster characters induced by generating extensions in a gentle algebra A, generalizing a result of Cerulli Irelli, Esposito, Franzen, Reineke. In the case where A is the gentle algebra of a triangulation T of an unpunctured marked surface, this provides a representation-theoretic interpretation of the exchange relations in the cluster algebra with principal coefficients in T. As an application, we interpret a formula that relates cluster variables of type B to cluster variables of type A in the symmetric module category of the algebras arising from special triangulations of a regular polygon. |
| title | A multiplication formula for cluster characters in gentle algebras |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2502.06410 |