广义Taft代数与Radford代数的双交叉积
Bicrossed products of generalized Taft algebras and Radford algebras
- Changzhou University（常州大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
在特征$p>0$的代数闭域上，对广义Taft代数$T_{N,n,\xi}$与Radford代数$R$的匹配对分类，得到$p\nmid N$时双交叉积为张量积Hopf代数、$p\mid N$时对应$p$个同构类的结果。
AI中文摘要：
在特征为$p>0$的代数闭域上，我们对广义Taft代数$T_{N,n,\xi}$与Radford代数$R$之间的所有匹配对进行分类。若$p\nmid N$，每个匹配对都是平凡的，对应的双交叉积是张量积Hopf代数；若$p\mid N$，匹配对由$\beta\in\mathbb F_p$参数化，双交叉积由明确的交叉关系描述。两个此类双交叉积作为Hopf代数同构当且仅当它们的参数相等，因此在该情形下恰好有$p$个同构类。
英文摘要：
Over an algebraically closed field of characteristic $p>0$, we classify all matched pairs between a generalized Taft algebra $T_{N,n,ξ}$ and the Radford algebra $R$. If $p\nmid N$, every matched pair is trivial, and the corresponding bicrossed product is the tensor product Hopf algebra. If $p\mid N$, matched pairs are parametrized by $β\in\mathbb F_p$, and the bicrossed products are described by explicit cross relations. Two such bicrossed products are isomorphic as Hopf algebras if and only if their parameters are equal; hence there are exactly $p$ isomorphism classes in this case.
