标题： 水母分区类别 显示英文标题

标题： Jellyfish partition categories

摘要： 对于每个正整数$n$，我们利用分区图的一般化定义引入了一个幺半范畴$\mathcal{JP}(n)$。当底域的特征要么为 0 要么至少为$n$时，我们证明$\mathcal{JP}(n)$在幺半范畴的意义上等价于一个满子范畴，该子范畴的对象是交错群$A_n$的自然$n$维置换表示的张量幂所在的范畴$\operatorname{Rep}(A_n)$。 显示英文摘要

摘要： For each positive integer $n$, we introduce a monoidal category $\mathcal{JP}(n)$ using a generalization of partition diagrams. When the characteristic of the ground field is either 0 or at least $n$, we show $\mathcal{JP}(n)$ is monoidally equivalent to the full subcategory of $\operatorname{Rep}(A_n)$ whose objects are tensor powers of the natural $n$-dimensional permutation representation of the alternating group $A_n$.