发表机构
Changzhou University（常州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画了指数为二的Hopf扩张为规范化二次扩张，用上循环和Ore数据描述其结构，并分类了特征2下维数16的非连通尖点Hopf代数。
AI 中文摘要
设$L$是代数闭域上的有限维尖点Hopf代数。我们建立了指数为二的扩张的内在刻画：每个包含$L$作为Hopf子代数且满足$H_0=L_0$和$\dim H=2\dim L$的Hopf代数$H$都是$L$的规范化二次扩张。对于固定的支撑$(g,h)$，此类扩张由余代数Hochschild $2$-上循环以及满足显式相容条件的Ore型数据$(\sigma,\delta,u,v)$描述。它们的同构类由$L$的规范变换和Hopf自同构的轨道参数化。作为应用，我们在特征$2$下分类了维数为$16$的非连通尖点Hopf代数，其无穷小编织为一维且图不是Nichols代数。
英文摘要
Let $L$ be a finite-dimensional pointed Hopf algebra over an algebraically closed field. We establish an intrinsic characterization of index-two extensions: every Hopf algebra $H$ containing $L$ as a Hopf subalgebra and satisfying $H_0=L_0$ and $\dim H=2\dim L$ is a normalized quadratic extension of $L$. For a fixed support $(g,h)$, such extensions are described by a coalgebra Hochschild $2$-cocycle together with Ore-type data $(σ,δ,u,v)$ satisfying explicit compatibility conditions. Their isomorphism classes are parameterized by the orbits of gauge transformations and Hopf automorphisms of $L$. As an application, we classify non-connected pointed Hopf algebras of dimension $16$ in characteristic $2$ with one-dimensional infinitesimal braiding whose diagram is not a Nichols algebra.
