论文标题
由对称群体的自动形态引起的同质谐音
Homogeneous quandles arising from automorphisms of symmetric groups
论文作者
论文摘要
Quandle是一个具有一个二进制操作的代数系统，但与一个组完全不同。 Quandle起源于结理论和与对称空间理论的良好关系，因此从这两个领域的角度来看都进行了充分研究。在本文中，我们调查了一种特殊的搜索，称为广义亚历山大·奎德尔斯$ q（g，ψ）$，该$由$ g $以及其组自动形态$ψ$定义。我们为广义的亚历山大·夸德尔斯（Alexander Quandles）开发了Quandle不变性。结果，我们证明，由对称组$ \ sf_n $引起的广义亚历山大·夸德斯（Alexander Quandles）与$ 3 \ leq n \ leq 30 $的$ \ sf_n $之间的一对一对应关系，以及$ n \ n \ neq neq 6,15 $，也讨论了$ n \ neq n = 6 $。
Quandle is an algebraic system with one binary operation, but it is quite different from a group. Quandle has its origin in the knot theory and good relationships with the theory of symmetric spaces, so it is well-studied from points of view of both areas. In the present paper, we investigate a special kind of quandles, called generalized Alexander quandles $Q(G,ψ)$, which is defined by a group $G$ together with its group automorphism $ψ$. We develop the quandle invariants for generalized Alexander quandles. As a result, we prove that there is a one-to-one correspondence between generalized Alexander quandles arising from symmetric groups $\Sf_n$ and the conjugacy classes of $\Sf_n$ for $3 \leq n \leq 30$ with $n \neq 6,15$, and the case $n=6$ is also discussed.
