论文标题
对称问题的同质表现
A homogeneous presentation of symmetric quandles
论文作者
论文摘要
一个问题是一个代数结构，其公理对应于结理论的雷德氏症动作。 S. Kamada介绍了一个具有良好相关性的困境的概念，后来被称为对称的问题。我们对对称难题的代数结构感兴趣。给定一个组$ g $，元素$ z $和某个子组$ h $，一个人可以获得困境。 D.乔伊斯（D. Joyce）表明，每个难题是这种难题的脱节结合。在本文中，给定一个$ g $，元素$ z，r $ in $ g $和某个亚组$ h $，我们构建了对称的Quandle。 futhermore，我们表明，每个对称的难题都是此类困境的不相交联合的同构。
A quandle is an algebraic structure whose axioms correspond to the Reidemeister moves of knot theory. S. Kamada introduced the notion of a quandle with a good involution, which is later called a symmetric quandle. We are interested in the algebraic structure of symmetric quandles. Given a group $G$, an element $z$ and a certain subgroup $H$, one can obtain the quandle. D. Joyce showed that every quandle is isomorphic to the disjoint union of such quandles. In this paper, given a group $G$, elements $z,r$ in $G$ and a certain subgroup $H$, we construct a symmetric quandle. Futhermore, we show that every symmetric quandle is isomorphic to the disjoint union of such quandles.
