About Hopf braces and crossed products

Ramón González Rodríguez; Brais Ramos Pérez

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arXiv · 2502.20919

About Hopf braces and crossed products

Ramón González Rodríguez·Brais Ramos Pérez

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Abstract

The present article represents a step forward in the study of the following problem: If $\mathbb{A}=(A_{1},A_{2})$ and $\mathbb{H}=(H_{1},H_{2})$ are Hopf braces in a symmetric monoidal category C such that $(A_{1},H_{1})$ and $(A_{2},H_{2})$ are matched pairs of Hopf algebras, then we want to know under what conditions the pair $(A_{1}\bowtie H_{1},A_{2}\bowtie H_{2})$ constitutes a new Hopf brace. We find such conditions for the pairs $(A_{1}\otimes H_{1},A_{2}\bowtie H_{2})$ and $(A_{1}\bowtie H_{1},A_{2}\sharp H_{2})$ to be Hopf braces, which are particular situations of the general problem described above, and we apply these results to study when the Drinfeld's Double gives rise to a Hopf brace.

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Ramón González Rodríguez, Brais Ramos Pérez. 2025-02-28. About Hopf braces and crossed products. https://arxiv.org/abs/2502.20919

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