Classification of Finite Alexander Quandles
Classification of Finite Alexander Quandles
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有限 Alexander Quandles 的分类
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发表时间：
2002
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通讯作者：
Sam Nelson
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作者：
Sam Nelson
两个元素个数相同的有限亚历山大quandle同构当且仅当它们的Z[t，t^-1]-子模Im（1-t）同构为模.这就给出了当形式为Z_n[t，t^-1]/（t-a）（其中gcd（n，a）=1）的亚历山大quandles（称为线性quandles）同构时的具体条件，以及当两个线性quandles是对偶的以及哪些线性quandles是连通的具体条件。我们应用这一结果得到一个程序的任何有限阶的亚历山大quandles的分类和作为一个应用程序，我们列出了不同的和连接的亚历山大quandles多达15个元素。
Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t,t^-1]-submodules Im(1-t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Z_n[t,t^-1]/(t-a) where gcd(n,a)=1 (called linear quandles) are isomorphic, as well as specific conditions on when two linear quandles are dual and which linear quandles are connected. We apply this result to obtain a procedure for classifying Alexander quandles of any finite order and as an application we list the numbers of distinct and connected Alexander quandles with up to fifteen elements.