Extension Theory for Braided-Enriched Fusion Categories
Extension Theory for Braided-Enriched Fusion Categories
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DOI：
10.1093/imrn/rnab133
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发表时间：
2019-10
影响因子：
1
通讯作者：
Corey Jones;S. Morrison;David Penneys;J. Plavnik
中科院分区：
文献类型：
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作者：
Corey Jones;S. Morrison;David Penneys;J. Plavnik
对于一个编织融合范畴$\mathcal{V}$，一个$\mathcal{V}$-融合范畴$\mathcal{C}$是一个融合范畴$\mathcal{F}: $ mathcal{V} \到Z(\mathcal{C})$。给定一个固定的$\mathcal{V}$-融合范畴$(\mathcal{C}, \mathcal{F})$和一个固定的$G$-分级扩展$\mathcal{C}\subseteq \mathcal{D}$作为一个普通的融合范畴，我们刻画了$\mathcal{D}$的充实$\ widdetilde {\mathcal{F}}:\mathcal{V} \到Z(\mathcal{D})$与$\mathcal{C}$的充实相容。我们证明了编织融合范畴$\mathcal{C}$的g -交叉扩展是$\mathcal{C}$对其自身正则富集的g -扩展。作为应用，我们将固定$G$分级融合范畴上的$G$交叉编织集合参数化为其中心的若干子范畴，推广了Nikshych关于融合范畴上编织的分类。
For a braided fusion category $\mathcal{V}$, a $\mathcal{V}$-fusion category is a fusion category $\mathcal{C}$ equipped with a braided monoidal functor $\mathcal{F}:\mathcal{V} \to Z(\mathcal{C})$. Given a fixed $\mathcal{V}$-fusion category $(\mathcal{C}, \mathcal{F})$ and a fixed $G$-graded extension $\mathcal{C}\subseteq \mathcal{D}$ as an ordinary fusion category, we characterize the enrichments $\widetilde{\mathcal{F}}:\mathcal{V} \to Z(\mathcal{D})$ of $\mathcal{D}$ that are compatible with the enrichment of $\mathcal{C}$. We show that G-crossed extensions of a braided fusion category $\mathcal{C}$ are G-extensions of the canonical enrichment of $\mathcal{C}$ over itself. As an application, we parameterize the set of $G$-crossed braidings on a fixed $G$-graded fusion category in terms of certain subcategories of its center, extending Nikshych’s classification of the braidings on a fusion category.