A criterion for the Müger centralizer of a fusion subcategory of a braided non-degenerate fusion category is given. Along the way we extend some identities on the space of class functions of a fusion category introduced by Shimizu (J Pure Appl Algebra 221(9):2338–2371, 2017). We also show that in a modular tensor category the product of two conjugacy class sums is a linear combination of conjugacy class sums with rational coefficients.

中文翻译：

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关键融合类别的共轭类和中心化器

给出了编织非退化融合类别的融合子类别的 Müger 扶正器的标准。在此过程中，我们在 Shimizu 引入的融合类别的类函数空间上扩展了一些恒等式（J Pure Appl Algebra 221(9):2338–2371, 2017）。我们还表明，在模张量类别中，两个共轭类和的乘积是共轭类和与有理系数的线性组合。