论文标题
$ d $图的怪物类型$（2η，η）$的轴向代数。我
Axial algebras of Monster type $(2η, η)$ for $D$ diagrams. I
论文作者
论文摘要
轴向代数是一类由基于群体产生的交换代数，具有半神经，并满足了规定的融合定律。 Hall，Rehren和Sheptorov在2015年引入了轴向代数，作为对Ivanov的Majorana代数的广泛概括，其公理源自Monster群的Griess代数的性质。 Matsuo介绍了Matsuo代数的类别，后来又由Hall，Rehren和Sheppectorov概括。 Matsuo代数$ m $由一组3条提议$ d $构建。 $ d $的元素是$ m $中的同性群，称为轴。特别是，$ m $是轴向代数的一个示例。众所周知，双轴，即Matsuo代数中两个正交轴的总和满足怪物类型的融合定律。该观察结果表明，由轴和双轴组成的集合可以在MATSUO代数中产生怪物类型的亚代词。许多作者广泛研究了与各种三个转置组相对应的亚词法。 在本文中，我们研究了由单个轴和两个双轴产生的原始亚代毛。我们将所有此类子代数分类为在九种可能的情况中的七个情况下，以了解与生成元素有关的3条置位图。我们还构建了几个无限的怪兽类型轴向代数，概括了我们的3生成代数。
Axial algebras are a class of commutative algebras generated by idempotents, with adjoint action semisimple and satisfying a prescribed fusion law. Axial algebras were introduced by Hall, Rehren, and Shpectorov in 2015 as a broad generalization of Majorana algebras of Ivanov, whose axioms were derived from the properties of the Griess algebra for the Monster group. The class of Matsuo algebras was introduced by Matsuo and later generalized by Hall, Rehren, and Shpectorov. A Matsuo algebra $M$ is built by a set of 3-transpositions $D$. Elements of $D$ are idempotents in $M$ and called axes. In particular, $M$ is an example of an axial algebra. It is known that double axes, i.e., sums of two orthogonal axes in a Matsuo algebra, satisfy the fusion law of Monster type. This observation shows that a set consisting of axes and double axes can generate a subalgebra of Monster type in the Matsuo algebra. Subalgebras corresponding to various series of 3-transposition groups are extensively studied by many authors. In this paper, we study primitive subalgebras generated by a single axis and two double axes. We classify all such subalgebras in seven out of nine possible cases for a diagram on 3-transpositions that are involved in the generating elements. We also construct several infinite series of axial algebras of Monster type generalizing our 3-generated algebras.
