Double centralizers of association schemes
Double centralizers of association schemes
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关联方案的双集中器
DOI：
10.1016/j.laa.2018.11.018
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发表时间：
2019
影响因子：
1.1
通讯作者：
Hanaki Akihide
中科院分区：
文献类型：
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作者：
Hanaki Akihide
关联方案的邻接代数被定义为任意域上的全矩阵代数的子代数。这里，关联方案是有限的并且不假定是可交换的。当全矩阵代数中的邻接代数的双中心化子与邻接代数重合时，我们称邻接代数具有双中心化性质。如果关联方案是 schurian，则邻接代数具有双中心化性质。我们将证明，如果关系数最多为 3，则邻接代数具有双中心化性质。另外，我们将看到一个不具有双扶正器属性的示例。
The adjacency algebra of an association scheme is defined as a subalgebra of the full matrix algebra over an arbitrary field. Here, association schemes are finite and not assumed to be commutative. When the double centralizer of the adjacency algebra in the full matrix algebra coincides with the adjacency algebra, we say that the adjacency algebra has the double centralizer property. If the association scheme is schurian, then the adjacency algebra has the double centralizer property. We will show that, if the number of relations is at most 3, then the adjacency algebra has the double centralizer property. Also, we will see an example which does not have the double centralizer property.