Abstract Fusion rings are a class of table algebras that generalize group rings with basis the group and character rings of a finite group with basis the irreducible characters. When considering the character ring of a group as a fusion ring, the usual degree of a character coincides with the degree map. Hence classifying fusion rings based on the degree set is a generalization of classifying groups based on the degrees of the irreducible characters. The main theorem classifies real fusion rings with degrees 1 and 4 such that all stabilizers have the same order.

中文翻译：

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具有 1 度和 4 度的真正融合环

摘要 融合环是一类以不可约字符为基的有限群的群和字符环的基推广群环的表代数。当将一个群的字符环视为融合环时，字符的通常度数与度数图重合。因此，基于度集对融合环进行分类是基于不可约特征的度对组进行分类的推广。主要定理用 1 级和 4 级对真实的聚变环进行分类，使得所有稳定器具有相同的阶数。