AI 中文总结
本文针对 quandle 的可容性问题，聚焦广义亚历山大 quandles，基于几何性质给出充分条件，推广了相关前期研究结论。
AI 中文摘要
quandle 的一个典型例子是共轭 quandle。若一个 quandle 同构于共轭 quandle，则称它是可容的。我们研究 quandle 的可容性问题，即判定给定 quandle 是否可容，尤其关注由群自同构定义的、带有 quandle 结构的广义亚历山大 quandles。本文基于 quandle 的几何性质给出可容性的充分条件：若每个代数连通分支中的每个对径集均由单个点构成，则该 quandle 是可容的。该结果推广了此前关于广义亚历山大 quandles 的研究结论。
英文摘要
A typical example of a quandle is the conjugation quandle. A quandle is said to be admissible if it is isomorphic to a conjugation quandle. We study the admissibility problem for quandles, that is, determining whether a given quandle is admissible. In particular, we focus on generalized Alexander quandles, which are groups equipped with quandle structures defined by group automorphisms. In this paper, we provide a sufficient condition for admissibility in terms of geometric properties of quandles: namely, if every antipodal set in each algebraically connected component consists of a single point, then the quandle is admissible. This result generalizes previous results on generalized Alexander quandles.
