根据局部顶点李代数的同态，可惟一地诱导出由它们分别构造所得的顶点代数之间同态的理论。

The important relationship between local vertex Lie algebra and vertex algebra is stated so that we could construct a vertex algebra from local vertex Lie algebra.

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讨论了半单广义顶点代数（相应地半单广义顶点算子代数）的若干性质，例如：这些代数的分解；

In this paper, some properties of semisimple generalized vertex algebras (resp. semisimple generalized vertex operator algebras), for example the decompositions of these algebras;

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理论已经逐步形成描述在有限群，标准化的形式和顶点算符代数之间的关系。

The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras.

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