论文标题
$ 3 $生成的轴向代数与最小的宫本集团
$3$-generated axial algebras with a minimal Miyamoto group
论文作者
论文摘要
轴向代数是最近引入的非缔合代数类别，具有自然相关的组，它概括了Griess代数和月光VOA的一些关键特征。 Sakuma的定理将八$ 2 $生成的轴向代数分类为Monster Type。在本文中，我们计算了几乎所有$ 3 $生成的轴向代数，其相关的宫本集团的相关轴向群是最小的$ 3 $生成的（其中包括最小$ 3 $生成的代数）。我们注意到，这项工作是独立于Mamontov，Staroletov和Whybrow进行的，并通过计算更多代数而不是假设原始性或相关的双线性形式来扩展其结果。
Axial algebras are a recently introduced class of non-associative algebra, with a naturally associated group, which generalise the Griess algebra and some key features of the moonshine VOA. Sakuma's Theorem classifies the eight $2$-generated axial algebras of Monster type. In this paper, we compute almost all the $3$-generated axial algebras whose associated Miyamoto group is minimal $3$-generated (this includes the minimal $3$-generated algebras). We note that this work was carried out independently to that of Mamontov, Staroletov and Whybrow and extends their result by computing more algebras and not assuming primitivity, or an associating bilinear form.
