共轭子广群的良好对合
Good involutions of conjugation subquandles
AI总结：
该研究针对带良好对合的广群分类难题，分析共轭子广群等的良好对合并得到数量界，实现相关计算算法、构造非对合对称广群族，完成低阶相关结构分类并证明范畴等价关系。
摘要：
由Taniguchi提出的带良好对合的广群分类是一个难题，在曲面纽结理论中有应用。我们针对共轭广群的子广群（包括所有核心广群）研究了这一问题，还探究了忠实架子的良好对合，特别得到了这类族中架子的良好对合数量的精确界。作为结果的应用，我们实现了计算共轭广群和核心广群所有良好对合的群论算法，给出了阶数不超过23的这类广群的相关数据；另一项应用是构造了无限族连通的非对合对称广群。我们还通过计算机搜索对阶数不超过8的对称与切触架子、广群及kei进行了分类。最后，我们证明了架子与切触架子之间的范畴等价，该等价诱导出对合架子、切触kei与对称kei之间的等价。
英文摘要：
Posed by Taniguchi, the classification of quandles with good involutions is a difficult question with applications to surface-knot theory. We address this question for subquandles of conjugation quandles, including all core quandles. We also study good involutions of faithful racks. In particular, we obtain sharp bounds on the number of good involutions of racks in these families. As an application of our results, we implement group-theoretic algorithms that compute all good involutions of conjugation quandles and core quandles; we provide data for those up to order 23. As another application, we construct infinite families of connected, noninvolutory symmetric quandles. We also classify symmetric and Legendrian racks, quandles, and kei up to order 8 using a computer search. Finally, we exhibit an equivalence of categories between racks and Legendrian racks that induces an equivalence between involutory racks, Legendrian kei, and symmetric kei.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
