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arXiv · 2305.11158

Coend elements of a braided Hopf algebra

Anh Tuong Nguyen
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Abstract

Let $H$ be a Hopf algebra in a braided rigid monoidal category $\mathcal{V}$ admitting a coend $C$. We define a ``coend element'' of $H$ to be a morphism from $C$ to $H$. We then study certain coend elements of $H$, which generalize important elements (e.g., pivotal and ribbon elements) of a finite dimensional Hopf algebra over a field. This builds on prior work of Brugui\`eres and Virelizier (2012) on $R$-matrices of braided Hopf algebras. As an application, we provide another description for pivotal and ribbon structures on the category $\mathcal{V}_H$ of $H$-modules.

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Anh Tuong Nguyen. 2023-05-18. Coend elements of a braided Hopf algebra. https://arxiv.org/abs/2305.11158

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