Constructions of the moonshine vertex operator algebra by using orbifold theories

通过这个研究项目，我们得到了一个新的基于二次空间的月光顶点算子代数的构造。作为应用，我们得到了Monster单群极大子群的一个新刻画。这是Golay码和Leech格的已知构造的模拟。从而得到了码、格和顶点算子代数之间的一个新的关系。此外，利用这种方法，我们将构造新的中心荷为24的全纯顶点算子代数。

By this research project, we obtain a new construction of the moonshine vertex operator algebra based on quadratic spaces. As an application, we obtain a new description of a maximal subgroup of the Monster simple group. This is an analog of the known constructions of the Golay code and Leech lattice. Hence we obtain a new relation among codes, lattices and vertex operator algebras. Moreover, by this approach, we would construct new holomorphic vertex operator algebras of central charge 24.