论文标题
niemeier lattices的Schellekens顶点操作员代数的系统轨道构造
Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
论文作者
论文摘要
我们提出了一个系统的，严格的，所有70个强烈理性的，全态顶点操作员代数$ v $ f $ central Charge 24，非零重量的空间$ v_1 $作为与24 niemeier lattice lattice lattice lattice lattice vertex opertor anggebras $ v_n $ v_n $ v_n $ and Automorphismorphismorphismphismorphismss Cyclic Orbifold构造$ \ operatatorName {aut}（v_n）$。 我们表明，如Arxiv：1910.04947所介绍的Niemeier lattice Vertex操作员代数的额外属性，其订单等于相应的外部自动性的命令，直到代数共轭性，这些自动形态正是广义的深孔，如Arxiv：1910.04947所述。 加上Arxiv中的构造：1708.05990和Arxiv：1910.04947，这给出了这些顶点操作员代数的三种不同的统一构造，它们通过$ \ operatateNORNAME {CO} {CO} _0 $ $ $的11个代数共轭类相关。 最后，通过考虑与226个短自动形态相关的逆Orbifold构造，我们给出了第一个系统的证据，证明了每一个强烈理性的，全体形状的顶点操作员代数$ v $ of Central Charter Chentral Chentral Charter Charter Chentral Charter 24具有非零重量的空间$ V_1 $ $ V_1 $由Lie Algebra Contruct of V _ $ v_1 $ with $ v_1 $ is唯一确定。
We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras $V$ of central charge 24 with non-zero weight-one space $V_1$ as cyclic orbifold constructions associated with the 24 Niemeier lattice vertex operator algebras $V_N$ and certain 226 short automorphisms in $\operatorname{Aut}(V_N)$. We show that up to algebraic conjugacy these automorphisms are exactly the generalised deep holes, as introduced in arXiv:1910.04947, of the Niemeier lattice vertex operator algebras with the additional property that their orders are equal to those of the corresponding outer automorphisms. Together with the constructions in arXiv:1708.05990 and arXiv:1910.04947 this gives three different uniform constructions of these vertex operator algebras, which are related through 11 algebraic conjugacy classes in $\operatorname{Co}_0$. Finally, by considering the inverse orbifold constructions associated with the 226 short automorphisms, we give the first systematic proof of the result that each strongly rational, holomorphic vertex operator algebra $V$ of central charge 24 with non-zero weight-one space $V_1$ is uniquely determined by the Lie algebra structure of $V_1$.
