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arXiv · 2204.02551

Ribbon Yetter--Drinfeld modules and tangle invariants

Kazuo Habiro·Yuka Kotorii
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Abstract

We define notions of pivotal and ribbon objects in a monoidal category. These constructions give pivotal or ribbon monoidal categories from a monoidal category which is not necessarily with duals. We apply this construction to the braided monoidal category of Yetter--Drinfeld modules over a Hopf algebra. This gives rise to the notion of ribbon Yetter--Drinfeld modules over a Hopf algebra, which form ribbon categories. This gives an invariant of tangles.

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Kazuo Habiro, Yuka Kotorii. 2022-04-06. Ribbon Yetter--Drinfeld modules and tangle invariants. https://arxiv.org/abs/2204.02551

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