论文标题
某个距离常规图的诺顿代数的非缔合性
Nonassociativity of the Norton Algebras of some distance regular graphs
论文作者
论文摘要
诺顿代数是一个距离常规图的特征空间，该图被称为诺顿产物的交换性非社交产物，该产品被定义为在此本特征空间上的入口产品的投影。诺顿代数在有限的群体理论中很有用，因为它们具有有趣的自动形态群体。我们为诺顿产品的非缔合性提供了精确的定量测量，该产品是基于该产品的公式，该产品是基于该产品在先前的工作中建立的莱夫斯坦，马尔多纳达多和penazzi的款项。我们的结果表明，除两种情况外，该产品尽可能非缔合性，一种是微不足道的消失案例，另一个是OEI上与整数序列A000975的连接，而Huang，Mickey，Mickey和Xu最近研究的所谓双重负操作。
A Norton algebra is an eigenspace of a distance regular graph endowed with a commutative nonassociative product called the Norton product, which is defined as the projection of the entrywise product onto this eigenspace. The Norton algebras are useful in finite group theory as they have interesting automorphism groups. We provide a precise quantitative measurement for the nonassociativity of the Norton product on the eigenspace of the second largest eigenvalue of the Johnson graphs, Grassman graphs, Hamming graphs, and dual polar graphs, based on the formulas for this product established in previous work of Levstein, Maldonado and Penazzi. Our result shows that this product is as nonassociative as possible except for two cases, one being the trivial vanishing case while the other having connections with the integer sequence A000975 on OEIS and the so-called double minus operation studied recently by Huang, Mickey, and Xu.
