Cluster characters for 2-Calabi-Yau Frobenius extriangulated categories (Q6612151)

Cluster algebras were introduced by \textit{S. Fomin} and \textit{A. Zelevinsky} [J. Am. Math. Soc. 15, No. 2, 497--529 (2002; Zbl 1021.16017)]. They are commutative algebras generated by the cluster variables, which are produced by mutating seeds. The relationship between cluster algebra and tilting theory was discovered by \textit{B. R. Marsh} et al. [Trans. Am. Math. Soc. 355, No. 10, 4171--4186 (2003; Zbl 1042.52007)], which has also been the main motivation to introduce the cluster category. Cluster categories are a class of 2-Calabi-Yau triangulated categories admitting cluster tilting objects and can be used to ``categorify'' cluster algebras. Thus, one needs to define a map from the considered category \(\mathcal{C}\) to the corresponding Laurent polynomial algebra, called the cluster character on \(\mathcal{C}\), such that it satisfies some properties and realizes the exchange relations in the cluster algebra. The present authors define the cluster characters for 2-Calabi-Yau Frobenius extriangulated categories with cluster tilting objects. This provides a unified framework of cluster characters in 2-Calabi Yau triangulated categories and 2-Calabi-Yau Frobenius exact categories given by \N\textit{Y. Palu} [Ann. Inst. Fourier 58, No. 6, 2221--2248 (2008; Zbl 1154.16008)] and \textit{C. Fu} and \textit{B. Keller} [Trans. Am. Math. Soc. 362, No. 2, 859--895 (2010; Zbl 1201.18007)], respectively.