格顶点算子超代数的自同构群
Automorphism Groups of Lattice Vertex Operator Superalgebras
DOI: 10.12677/PM.2022.124053, PDF,   
作者: 崔志广：青岛大学，数学与统计学院，山东 青岛
关键词: 正定整格；顶点算子超代数；自同构群；Lattice； Vertex Operator Superalgebra； Automorphism Group
摘要: 本文主要研究由正定整格构造的格顶点算子超代数的自同构群的结构，通过正定整格的中心扩张得出的等距自同构和格顶点算子超代数的结构以及李代数的共轭定理，证明出格顶点算子超代数的自同构群是内导子诱导的自同构群与正定整格的等距自同构诱导的自同构群的积。
Abstract: This paper aims to give a total description of the automorphism group of the vertex operator superalgebra associated to a positive definite integral lattice. By the isometries coming from the centrale extension of the positive definite integral lattice, the structure of the lattice vertex oper-ator superalgebra and the conjugacy theorem from Lie algebra, we get that the automorphism group of the lattice vertex operator superalgebra is the product of the automorphism group deduced from inner derivations and the automorphism group deduced from isometries of the lattice.
文章引用：崔志广. 格顶点算子超代数的自同构群[J]. 理论数学, 2022, 12(4): 473-481. https://doi.org/10.12677/PM.2022.124053

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