论文标题
融合类别的规范，跟踪和正式代码
Norm, trace, and formal codegrees of fusion categories
论文作者
论文摘要
我们使用正式编码的Galois共轭物的产品（规范）和总和（痕迹）证明了融合类别理论的几个结果。首先，我们证明存在有限的融合类别，其全球维度具有固定规范的等效性。此外，除两个例外外，所有具有无正式标准的球形融合类别的正式代码都是理性整数。这意味着，除三个例外，每个球形编织融合类别的全球维度具有主要规范。发生例外的原因与描述较小的绝对痕迹的完全积极的代数整数的经典schur-siegel-smyth有关。
We prove several results in the theory of fusion categories using the product (norm) and sum (trace) of Galois conjugates of formal codegrees. First, we prove that finitely-many fusion categories exist up to equivalence whose global dimension has a fixed norm. Furthermore, with two exceptions, all formal codegrees of spherical fusion categories with square-free norm are rational integers. This implies, with three exceptions, that every spherical braided fusion category whose global dimension has prime norm is pointed. The reason exceptions occur is related to the classical Schur-Siegel-Smyth problem of describing totally positive algebraic integers of small absolute trace.
