A commutativity condition for subsets in quandles --- a generalization of antipodal subsets
A commutativity condition for subsets in quandles --- a generalization of antipodal subsets
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Quantles 中子集的交换性条件——对映子集的推广
DOI：
10.1090/conm/777/15631
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Hiroshi Tamaru
中科院分区：
文献类型：
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作者：
Akira Kubo;Mika Nagashiki;Takayuki Okuda;Hiroshi Tamaru
本文引入了quandles中子集的交换性条件，我们称之为s-交换性。注意quandles可以看作是对称空间的推广，而s-交换子集的概念是对映子集的推广。研究了quandles中的极大s-交换子集，并证明了它们具有一些很好的性质。作为一个例子，quandle中的任何最大交换子集都是子quandle。我们还确定最大的s-交换子集领域，射影空间，二面角quandles。在这些困境中，极大s-交换子集变成唯一的自同构。
In this paper, we introduce some commutativity condition for subsets in quandles, which we call the s-commutativity. Note that quandles can be regarded as a generalization of symmetric spaces, and the notion of s-commutative subsets is a generalization of antipodal subsets. We study maximal s-commutative subsets in quandles, and show that they have some nice properties. As one example, any maximal scommutative subsets in quandles are subquandles. We also determine maximal s-commutative subsets in spheres, projective spaces, and dihedral quandles. In these quandles, maximal s-commutative subsets turn out to be unique up to automorphisms.