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arXiv · 2412.16722

The Tannakian radical and the mantle of a braided fusion category

Jason Green·Dmitri Nikshych
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Abstract

We define the Tannakian radical of a braided fusion category $\mathcal{C}$ as the intersection of its maximal Tannakian subcategories. The localization of $\mathcal{C}$ corresponding to the Tannakian radical, termed the mantle of $\mathcal{C}$, admits a canonical central extension that serves as a complete invariant of $\mathcal{C}$. The mantle has a trivial Tannakian radical, and we refer to braided fusion categories with this property as reductive. We investigate the properties and structure of reductive categories and prove several classification results.

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Jason Green, Dmitri Nikshych. 2024-12-21. The Tannakian radical and the mantle of a braided fusion category. https://arxiv.org/abs/2412.16722

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