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arXiv · 2502.06410

A multiplication formula for cluster characters in gentle algebras

Azzurra Ciliberti
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Abstract

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.

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Azzurra Ciliberti. 2025-02-10. A multiplication formula for cluster characters in gentle algebras. https://doi.org/10.1093/imrn%2Frnaf272

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