论文标题
约旦和怪物类型的轴向代数
Axial algebras of Jordan and Monster type
论文作者
论文摘要
轴向代数是一类非缔合性交换代数，其特性是根据融合定律定义的。当对融合定律进行分级时，代数具有自然相关的自动形态，因此轴向代数与群体理论固有地相关。示例包括大多数约旦代数和怪物零星简单组的Griess代数。 在这项调查中，我们介绍轴向代数，讨论其结构特性，然后集中在两个特定类别上：约旦和怪物类型的代数，它们富含与简单组相关的示例。
Axial algebras are a class of non-associative commutative algebras whose properties are defined in terms of a fusion law. When this fusion law is graded, the algebra has a naturally associated group of automorphisms and thus axial algebras are inherently related to group theory. Examples include most Jordan algebras and the Griess algebra for the Monster sporadic simple group. In this survey, we introduce axial algebras, discuss their structural properties and then concentrate on two specific classes: algebras of Jordan and Monster type, which are rich in examples related to simple groups.
