ABSTRACT

Let $(H,\cdot ,\circ )$ be a Hopf brace. We first show that the category of left compatible modules over $(H,\cdot ,\circ )$ is a tensor category. Next, we show that its Drinfeld centre is equivalent to the category ${}_{\mathbb{H}}^{H^{\prime }}\mathcal{Y}\mathcal{D}$ of left Yetter–Drinfeld modules over $(H,\cdot ,\circ )$ as a braided tensor category. Finally, we show that Radford's biproduct $(R\mathrm{♯}H,\cdot )$ and $(R\mathrm{♯}{H}_{\circ },\circ )$ constitute a Hopf brace, where R is a Hopf algebra in ${}_{\mathbb{H}}^{H^{\prime }}\mathcal{Y}\mathcal{D}$. This presents some new method to construct Hopf braces.

中文翻译：

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从 Hopf 大括号构建编织张量类别

摘要

让$(H,\cdot ,\circ )$做一个 Hopf 支架。我们首先表明左兼容模块的类别超过$(H,\cdot ,\circ )$是张量范畴。接下来，我们证明它的 Drinfeld 中心等价于类别${}_{\mathbb{H}}^{H^{\text{'}}}\mathcal{是}\mathcal{D}$左侧的 Yetter-Drinfeld 模块$(H,\cdot ,\circ )$作为编织张量类别。最后，我们证明了 Radford 的二乘$(R\mathrm{♯}H,\cdot )$和$(R\mathrm{♯}{H}_{\circ },\circ )$构成一个 Hopf 大括号，其中R是一个 Hopf 代数${}_{\mathbb{H}}^{H^{\text{'}}}\mathcal{是}\mathcal{D}$. 这提出了一些构建 Hopf 大括号的新方法。