论文标题
为什么怪物顶点代数的对称性形成有限的简单组？
Why do the symmetries of the monster vertex algebra form a finite simple group?
论文作者
论文摘要
连同他们的1988年构建Monster Vertex代数$ v^\ Natural $，Frenkel，Lepowsky和Meurman一起，表明，最大的零星简单组（称为Fischer-Griess Monster）形成了对称对称性的对称性小组，由无限尺寸的尺寸代数对象组成，其构造的构造是由理论上的物理学激励的。但是，对称群体实际上是有限且简单的事实，最终依赖于Griess在怪物作品中使用的高度非平凡的群体理论结果。我们证明了$ v^\天然$的自动形态群体的某些特性，最值得注意的是，它是有限和简单的，使用了顶点操作员代数理论的最新发展，但主要是19世纪的群体理论。
Together with their 1988 construction of the monster vertex algebra $V^\natural$, Frenkel, Lepowsky, and Meurman showed that the largest sporadic simple group, known as the Fischer-Griess monster, forms the symmetry group of an infinite dimensional algebraic object whose construction was motivated by theoretical physics. However, the fact that the symmetry group is in fact finite and simple ultimately relied on highly non-trivial group-theoretic results used in Griess's work on the monster. We prove some properties of the automorphism group of $V^\natural$, most notably that it is is finite and simple, using recent developments in the theory of vertex operator algebras, but mostly 19th century group theory.
