论文标题
关于阳性特征低等级的对称融合类别的评论
Remarks on symmetric fusion categories of low rank in positive characteristic
论文作者
论文摘要
我们在特征$ p \ geq 5 $中为对称融合类别的等级提供了较低的界限。我们证明，第二个ADAMS操作$ψ_2$不是任何非平凡的对称融合类别的身份，而满足$ψ_2^a =ψ_2^a =ψ_2^{a-1} $的对称融合类别对于某些正integer $ a $ a $ a $是超级tannakian。作为一个应用程序，我们将所有等级3的对称融合类别和等级4的所有对称融合类别与两个自我双重简单对象进行了分类。
We give lower bounds for the rank of a symmetric fusion category in characteristic $p\geq 5$ in terms of $p$. We prove that the second Adams operation $ψ_2$ is not the identity for any non-trivial symmetric fusion category, and that symmetric fusion categories satisfying $ψ_2^a=ψ_2^{a-1}$ for some positive integer $a$ are super Tannakian. As an application, we classify all symmetric fusion categories of rank 3 and those of rank 4 with exactly two self dual simple objects.
