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arXiv · 1912.01392

Hopf brace, braid equation and bicrossed coproduct

Huihui Zheng·Fangshu Li·Tianshui Ma·Liangyun Zhang
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Abstract

In this paper, we mainly give some equivalent characterisations of Hopf braces, show that the category $\mathcal{CB}(A)$ of Hopf braces is equivalent to the category $\mathcal{C}(A)$ of bijective 1-cocycles, and prove that the category $\mathcal{CB}(A)$ of Hopf braces is also equivalent to the category $\mathcal{M}(A)$ of Hopf matched pairs. Moreover, we construct many more Hopf braces on polynomial Hopf algebras, Long copaired Hopf algebras and Drinfel'd doubles of finite dimensional Hopf algebras, and give a sufficient and necessary condition for a given bicrossed coproduct $A\bowtie H$ to be a Hopf brace if $A$ or $H$ is a Hopf brace.

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Huihui Zheng, Fangshu Li, Tianshui Ma, Liangyun Zhang. 2019-12-03. Hopf brace, braid equation and bicrossed coproduct. https://arxiv.org/abs/1912.01392

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