The structure of 3C-algebra and 5A-algebra constructed by Lam-Yamada-Yamauchi is studied and the uniqueness of the vertex operator algebra structure of these two algebras is established. We also give the fusion rules for these two algebras.

中文翻译：

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3C-代数和5A-代数的VOA结构的独特性

研究了Lam-Yamada-Yamauchi构造的3C-代数和5A-代数的结构，并建立了这两个代数的顶点算子代数结构的唯一性。我们还给出了这两个代数的融合规则。