论文标题
三角棱镜方程和分类
Triangular Prism Equations and Categorification
论文作者
论文摘要
我们介绍了融合类别的三角形棱镜方程，在球形案例中证明了它们与五角大楼方程的等效性，并改变了基础。这些方程提供了通过本地化来管理复杂性的宝贵见解。此外，我们建立了Z. Wang的猜想的增强版本，内容涉及关键融合类别中的第二个Frobenius-Schur指标。作为应用程序，我们介绍了新的分类标准，并完成了统一1-Frobenius简单积分融合类别的分类，直至8级和FPDIM 20000。
We present the triangular prism equations for fusion categories, demonstrating their equivalence to the pentagon equations in the spherical case, modulo a change of basis. These equations offer valuable insights for managing complexity through localization. Additionally, we establish an enhanced version of Z. Wang's conjecture regarding the second Frobenius-Schur indicator in pivotal fusion categories. As applications, we introduce new categorification criteria and complete the classification of unitary 1-Frobenius simple integral fusion categories up to rank 8 and up to FPdim 20000.
