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arXiv · 2312.10173

On bicrossed modules of Hopf algebras

Xiao Han
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Abstract

We use Hopf algebroids to formulate a notion of a noncommutative and non-cocommutative Hopf 2-algebra. We show how these arise from a bicrossproduct Hopf algebra with Peiffer identities. In particular, we show that for a Hopf algebra $H$ with bijective antipode, the mirror bicrossproduct Hopf algebra $H\triangleright\!\!\!\blacktriangleleft H_{cop}$ is a Hopf 2-algebra. We apply the theorem on Sweedler's Hopf algebra as an example.

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Xiao Han. 2023-12-15. On bicrossed modules of Hopf algebras. https://arxiv.org/abs/2312.10173

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