n-边形的中心化子代数
The Centralizer Algebra of the Ordinary n-Cycle
DOI: 10.12677/pm.2024.143088, PDF,   
作者: 赵 伟：河北地质大学数理教学部，河北 石家庄
关键词: n-边形；中心化子代数；Terwilliger代数；Ordinary n-Cycle； Centralizer Algebra； Terwilliger Algebra
摘要: 用符号Cn表示顶点集为X的n-边形。任意取定顶点x∈X，用A:=A(x)表示关于点x的稳定子群(Cn的自同构群中的子群)的中心化子代数。在本文中，我们首先通过点x的稳定子群在集合X×X上的作用构造出A的一组基。然后，给出A的三个子代数使得它们的向量空间直和恰好是A。最后，我们证明代数A和代数T相等，这里T:=T(x)表示Cn的关于点x的Terwilliger代数。
Abstract: Let Cn denote the Ordinary n-cycle with vertex set X. Fix any vertex x∈X, and let A:=A(x) denote the centralizer algebra of the stabilizer of x in the automorphism group of Cn. In this paper, we first give a basis of A by this stabilizer acting on X×X. Moreover, we give three subalgebras of A such that their direct sum is just A as vector space of matrices. Finally, we show that the two algebras A and T coincide, where T:=T(x) denotes the Terwilliger algebra of Cn with respect to x.
文章引用：赵伟. n-边形的中心化子代数[J]. 理论数学, 2024, 14(3): 89-99. https://doi.org/10.12677/pm.2024.143088

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