The Drinfeld centre of a symmetric fusion category is 2-fold monoidal
The Drinfeld centre of a symmetric fusion category is 2-fold monoidal
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对称融合范畴的 Drinfeld 中心是 2 重幺半群
DOI：
10.1016/j.aim.2020.107090
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发表时间：
2017
影响因子：
1.7
通讯作者：
T. Wasserman
中科院分区：
文献类型：
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作者：
T. Wasserman
证明了特征为零的代数闭域上对称融合范畴的Drinfeld中心是双2重么半范畴。也就是说，它带有两个么整结构，卷积和对称张量积，这两个结构是相互关联的双极单整函子。此外，我们还证明了卷积张量积和对称张量积的辫子和对称性与这种双峰结构是相容的。我们在不涉及对称融合范畴的Tannaka对偶的情况下建立了这些性质。这样做的好处是，所有的构式都是纯粹根据融合范畴结构进行的，使得结果很容易在其他上下文中使用。
We show that the Drinfeld centre of a symmetric fusion category over an algebraically closed field of characteristic zero is a bilax 2-fold monoidal category. That is, it carries two monoidal structures, the convolution and symmetric tensor products, that are bilax monoidal functors with respect to each other. We additionally show that the braiding and symmetry for the convolution and symmetric tensor products are compatible with this bilax structure.We establish these properties without referring to Tannaka duality for the symmetric fusion category. This has the advantage that all constructions are done purely in terms of the fusion category structure, making the result easy to use in other contexts.