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arXiv · 2603.22932

On modules over a Hopf brace

Ramón González Rodríguez·Brais Ramos Pérez·Ana Belén Rodríguez Raposo
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Abstract

Let $\mathbb{H}=(H_{1},H_{2})$ be a Hopf brace in a symmetric monoidal category ${\sf C}$. In this article it is proved that the category of modules over $\mathbb{H}$ is isomorphic to the category of modules over the smash product algebra $H_{1}\sharp H_{2}$. Furthermore, the category of modules over $\mathbb{H}$ in the sense of Zhu is characterized by the condition that a certain action lies in the cocommutativity class of $H_{2}$.

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Ramón González Rodríguez, Brais Ramos Pérez, Ana Belén Rodríguez Raposo. 2026-03-24. On modules over a Hopf brace. https://arxiv.org/abs/2603.22932

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