从非对称3秩关联方案构造非交换8秩关联方案对

arXiv: Combinatorics Pub Date : 2019-11-21 DOI:10.5802/alco.167

A. Hanaki, Masayoshi Yoshikawa

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引用次数: 1

摘要

我们从一个秩3的非对称关联方案构造了一对秩8的非交换关联方案。对于这对组合，两种关联方案具有相同的字符表，但Frobenius-Schur指标不同。这种情况类似于二面体基团和8阶四元数的对偶。我们还确定了它们在有理数域上的邻接代数的结构。

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A construction of pairs of non-commutative rank 8 association schemes from non-symmetric rank 3 association schemes

We construct a pair of non-commutative rank 8 association schemes from a rank 3 non-symmetric association scheme. For the pair, two association schemes have the same character table but different Frobenius-Schur indicators. This situation is similar to the pair of the dihedral group and the quaternion group of order 8. We also determine the structures of adjacency algebras of them over the rational number field.

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arXiv: Combinatorics

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