Graded Frobenius cluster categories (Q1753983)

The authors study multi-gradings for generalized cluster categories. They extend earlier work by \textit{J. E. Grabowski} [J. Algebr. Comb. 42, No. 4, 1111--1134 (2015; Zbl 1333.13032)] to certain Frobenius categories which are categorifications of cluster algebras with non-trivial coefficients. Examples of these categories are the Grassmannian cluster categories of \textit{B. T. Jensen} et al. [Proc. Lond. Math. Soc. (3) 113, No. 2, 185--212 (2016; Zbl 1375.13033)] as well as categories considered by \textit{A. B. Buan} et al. [Compos. Math. 145, No. 4, 1035--1079 (2009; Zbl 1181.18006)], and \textit{C. Geiss} et al. [in: Trends in representation theory of algebras and related topics. Proceedings of the 12th international conference on representations of algebras and workshop (ICRA XII). Zürich: European Mathematical Society (EMS). 253--283 (2008; Zbl 1203.16014)]. The authors prove that the degrees are additive on short exact sequences and compatible with the cluster character and mutations.