月光型顶点算子代数是一类具有特殊性质的顶点算子代数，重要的月光顶点算子代数即是其中一类。在本研究项目中，我们主要研究Greiss代数同构于Jordan代数的月光型顶点算子代数。基于Ashihara、Miyamoto 以及林正洪等人的结果，和申请者本人之前的一些工作，我们进一步研究Greiss代数同构于Jordan代数的月光型顶点算子代数的相关构造、结构以及表示，同时计算它们的特征公式并分析其几何意义。

The moonshine type VOAs are certain kinds of VOAs satisfying some special properties, in which the important `moonshine VOA' being one of the examples. In this research program, we focus on the moonshine type VOAs whose Greiss algebras are Jordan algebras. Based on the work of Ashihara, Miyamoto, Lam, etc., and some previous results obtained by the applicant, we will make a further study on the construction and algebraic structure of the moonshine type VOAs whose Greiss algebras are Jordan algebras, together with their representations. In the meantime we compute the character formulas of these VOAs and discuss their geometric meanings.