Construction and classification of holomorphic vertex operator algebras of central charge 24

中心电荷24的全纯顶点算子代数的构造与分类是一个著名的开放问题。1993年预测了71个中心电荷为24的全纯顶点算子代数的存在性，1996年明确构造了39个全纯顶点算子代数。在本研究中，我们利用框架顶点算子代数理论和轨道构造构造了9个新的矩阵。由于其他研究者获得了11个新的全纯顶点算子代数，我们知道存在59个中心电荷为24的全纯顶点算子代数。这使得施工问题有所进展。此外，我们还证明了中心电荷24的全纯框架顶点算子代数的存在。这在分类问题上取得了进展。

The construction and classification of holomorphic vertex operator algebras of central charge 24 is a famous open problem. In 1993 existence of 71 holomorphic vertex operator algebras of central charge 24 is predicted, and in 1996, 39 of them are explicitly constructed.In this research, we construct nine new ones by using framed vertex operator algebra theory and orbifold construction. Since eleven new ones are obtained by other researchers, we know that there exist 59 holomorphic vertex operator algebras of central charge 24. This makes progress in the construction problem. In addition, we prove that there exist exactly 56 holomorphic framed vertex operator algebras of central charge 24. This makes progress in the classification problem.