Vertex operator algebras with group action

在1997年，一个与二秩A型根格相关联的顶点算子代数的具有三阶对称性的子代数被发现，并研究了它的性质。特别是确定了它的自同构群，并对它的单模进行了分类。结果写在联合文件三元码和顶点算子代数。这种顶点算子代数与Monster模之间的关系还有待研究。此外，从顶点算子代数的角度研究了Borwein型恒等式.结果写在一个联合文件Borwein身份和顶点算子algebrus.In 1998年所有最高权向量的重量最多为两个顶点算子代数与根格的A型进行了分类。最高权向量是重要的，因为一旦它们是已知的，那么顶点算子代数可以被分解为Virasoro顶点算子代数的张量积的简单模的直和。虽然不是所有的最高权向量都是已知的，但关于顶点算子代数的结构的许多信息可以从权最多为2的最高权向量中获得。例如，通过使用这些最高权重向量构造具有4阶对称性的顶点算子代数。最近所有的最高权重向量的情况下，秩三根格的类型A.为了推广这一结果的任意秩的根格，将需要一个新的想法。

In 1997 a subalgebra having order three symmetry of a vertex operator algebra associated with a rank two root lattice of type A was discovered and its properties were studied. In particular its automorphism group was determined and its simple modules were classified. The results were written in a joint paper Ternary codes and vertex operator algebras. Relations between this vertex operator algebra and the Monster module still remain to be studied. Moreover, Borwein type identity was studied from a point of view of vertex operator algebra. The results were written in a joint paper Borwein identity and vertex opertor algebras.In 1998 all highest weight vectors with weight at most two of a vertex operator algebra associated with a root lattice of type A were classified. Highest weight vectors are important, because once they are known then a vertex operator algebra can be decomposed into a direct sum of simple modules for a tensor product of Virasoro vertex operator algebras. Although not all highest weight vectors are known, much information about the structure of the vertex operator algebra can be obtained from highest weight vectors with weight at most two. For example, a vertex operator algebra having a symmetry of order 4 was constructed by using these highest weight vectors. Recently all highest weight vectors were classified in the case of rank three root lattice of type A.In order to generalize this result to a root lattice of arbitrary rank, a new idea would be required.