顶点算子代数结构的唯一性
Uniqueness of Vertex Operator Algebras
DOI: 10.12677/pm.2026.164119, PDF,   
作者: 顾钰晗：青岛大学数学与统计学院，山东 青岛
关键词: 顶点算子代数；唯一性；辫子矩阵；融合律；Vertex Operator Algebra； Uniqueness； Braiding Matrix； Fusion Rule
摘要: 本文研究了一列顶点算子代数结构的唯一性。这类顶点算子代数的来源是GKO构造，性质由Virasoro顶点算子代数的酉序列及其模决定，具有较好的条件，并且它们还是3A代数与6A代数的推广。它们的顶点算子代数结构由一些模之间的缠结算子决定，而本文证明了只要相关模的融合律不为零，则这一顶点算子代数结构中对应的分量部分也必为非零。本文主要考察了融合律与辫子矩阵等性质，并利用这些方法完成了证明。
Abstract: This paper studies the uniqueness of a series of vertex operator algebra structures. These types of vertex operator algebras originate from the GKO construction, with their properties determined by unitary series of the Virasoro vertex operator algebraa and their modules. They have favorable conditions and are also generalizations of the 3A and 6A algebras. The vertex operator algebra structure is determined by the intertwining operators between certain modules, and this paper proves that as long as the fusion rules of the relevant modules are non-zero, the corresponding components in the vertex operator algebra structure must also be non-zero. The paper primarily uses properties such as fusion rules and braid matrices, and uses these methods to complete the proof.
文章引用：顾钰晗. 顶点算子代数结构的唯一性[J]. 理论数学, 2026, 16(4): 333-342. https://doi.org/10.12677/pm.2026.164119

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