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和分类是一个著名的公开问题。1993年预测了中心电荷为24的71个全纯顶点算子代数的存在，1996年明确构造了其中39个全纯顶点算子代数.在这一研究中，我们利用有框架的顶点算子代数理论和orboold结构构造了9个新的全纯顶点算子代数.由于其他研究者得到了11个新的全纯顶点算子代数，我们知道有59个中心电荷为24的全纯顶点算子代数。这在建设问题上取得了进展。此外，我们证明了中心电荷为24的全纯框架顶点算子代数恰好存在56个。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.