Gerald Hoehn, Nils R. Scheithauer
We use a Z_2-orbifold of the vertex operator algebra associated to the Niemeier lattice with root lattice A_3^8 and the no-ghost theorem of string theory to construct a generalized Kac-Moody algebra. Borcherds' theory of automorphic products allows us to determine the simple roots and identify the algebra with the fake baby monster Lie algebra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this article we prove that the full automorphism group of the baby-monster vertex operator superalgebra constructed by Hoehn is isomorphic to 2xB, where B is the baby-monster sporadic finite simple group and determine irreducible modules for the baby-monster vertex operator algebra. Our result has many corollaries. In particular, we can prove that the Z_2-orbifold construction with respect to a 2A-involution of the Monster applied to the moonshine vertex operator algebra yields the moonshine vertex operator algebra itself again.
In this paper we consider several problems in the theory of automorphic products and generalized Kac--Moody algebras proposed by Borcherds in 1995. We show that the denominator of the fake monster algebra defines the unique holomorphic Borcherds product of singular weight on a maximal lattice. We give a full classification of symmetric holomorphic Borcherds products of singular weight on lattices of prime level. Finally we prove that all twisted denominator identities of the fake monster algebra arise as the Fourier expansions of Borcherds products of singular weight at a certain cusp. The pro…
Introduction to Vertex Algebras, Borcherds Algebras, and the Monster Lie Algebra
顶点代数的理论构成了共形场论的代数起源的数学上严格的公理化公式。在这种情况下，Borcherds代数作为顶点代数的某些“物理”子空间而出现。本文旨在对这一迅速发展的学科作一个教学介绍。基于形式演算的机制，给出了顶点代数的公理化定义。通过导出这些公理的重要蕴涵，讨论了它们与共形场论的联系。特别是，许多明确的计算提出了突出的作用，Jacobi单位公理顶点代数。作为一类具体的例子，构造了偶格上的顶点代数，并详细说明了仿射李代数和伪Monster李代数是如何自然出现的。这就引出了Borcherds代数作为广义卡茨-穆迪代数的抽象定义及其基本性质。最后，从量子理论对称性的角度分析了最简单的一般Borcherds代数的结果，并概述了Monster李代数的构造。
Realizations of the Monster Lie algebra
我们研究广义Kac-Moody李代数（或Borcherds代数）及其标准模的理论。证明了无相互正交虚单根代数（包括Borcherds Monster李代数$\frak m$）是如何由某个Kac-Moody子代数和它的模自然地构造出来的，并观察到广义卡茨-穆迪代数的某些广义Verma（诱导）模是标准模，因而是不可约的.特别地，从Monster群$M$的月光模出发，构造了一个特定的$\{frak gl}_2$ -和$M$ -模，其上的张量代数具有$\frak m$的不可约模的自然结构，它被实现为这个张量代数上的算子的显式指定的$M$ -协变李代数.进一步利用$\frak m$的大自由子代数的存在性，简化了Borcherds关于月光模的McKay-Thompson级数的Conway-Norton证明.这些系列的系数满足自然的递归关系（复制公式）相当于，但不同，由Borcherds获得。
Symmetries of Borcherds algebras
本文研究了伯克赫德代数的构造及其在弦理论中的应用，探讨了怪兽李代数$\mathfrak m_g$的对称性和相关开放问题。
E7 part: In this paper, we study McKay's E7 observation on the Baby Monster. By investigating so called derived c=7/10 Virasoro vectors, we show that there is a natural correspondence between dihedral subgroups of the Baby Monster and certain subalgebras of the Baby Monster vertex operator algebra which are constructed by the nodes of the affine E7 diagram. This allows us to reinterpret McKay's E7 observation via the theory of vertex operator algebras. For a class of vertex operator algebras including the Moonshine module, we will show that the product of two Miyamoto involutions associated to…
We introduce the Z_2-extended Griess algebra of a vertex operator superalgebra with an involution and derive the Matsuo-Norton trace formulae for the extended Griess algebra based on conformal design structure. We illustrate an application of our formulae by reformulating the one-to-one correspondence between 2A-elements of the Baby-monster simple group and N=1 c=7/10 Virasoro subalgebras inside the Baby-monster vertex operator superalgebra.
Any finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group, with the possible exception of the Fischer groups Fi22, the Baby Monster B and the Monster M, is a group algebra.
Selbstduale Vertexoperatorsuperalgebren und das Babymonster (Self-dual Vertex Operator Super Algebras and the Baby Monster)
本文研究自对偶顶点算子超代数，构造中心荷23.5的较短月光模，宝贝怪兽群作用其上，并引入极值SVOAs概念，给出存在性结果。
We show using Borcherds products that for any fixed-point free automorphism of the Leech lattice satisfying a "no massless states" condition, the corresponding cyclic orbifold of the Leech lattice vertex operator algebra is isomorphic to the Monster vertex operator algebra. This induces an "orbifold duality" bijection between algebraic conjugacy classes of fixed-point free automorphisms of the Leech lattice satisfying this condition and algebraic conjugacy classes of non-Fricke elements in the Monster. We use the duality to show that non-Fricke Monstrous Lie algebras are Borcherds-Kac-Moody Li…
The Group of Symmetries of the shorter Moonshine Module
本文证明了较短月光模（Baby Monster顶点算子超代数）的自同构群为Baby Monster单群与2阶循环群的直积。
We show that every finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group is a group algebra, except for the Fischer group Fi22, the Baby Monster and the Monster. For these three groups, we give a short list of irreducible Yetter-Drinfeld modules whose Nichols algebra is not known to be finite-dimensional.
Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $M_{23}$
本研究针对Borcherds提出的相关李代数自然构造问题，证明了Scheithauer分类的十个无平方因子水平格上奇异权完全反射自守乘积型Borcherds-Kac-Moody代数，可统一实现为合适顶点代数的BRST上同调。
A Magnus group construction for a class of Borcherds algebras
本文提出了一类Borcherds代数的Magnus群构造方法，并展示了该构造在不同基选择下的同构性，应用于多个具体例子。
This dissertation answers some of the questions raised in Borcherds' papers on Moonshine and Lorentzian reflection groups. We prove (assuming an open conjecture of Burger, Li and Sarnak) that a Lorentzian reflection group with Weyl vector is associated to a vector-valued modular form. This result allows us to establish a folklore conjecture that the maximal dimension of a Lorentzian reflection group with Weyl vector is 26. In the case of elementary lattices, we show that these vector-valued forms can be obtained by inducing scalar-valued forms. This allows us to explain the critical signatures…
Starting from Borcherds' fake monster Lie algebra we construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including AE3.
Given a holomorphic $C_2$-cofinite vertex operator algebra $V$ with graded dimension $j-744$, Borcherds's proof of the monstrous moonshine conjecture implies any finite order automorphism of $V$ has graded trace given by a "completely replicable function", and by work of Cummins and Gannon, these functions are principal moduli of genus zero modular groups. The action of the monster simple group on the monster vertex operator algebra produces 171 such functions, known as the monstrous moonshine functions. We show that 154 of the 157 non-monstrous completely replicable functions cannot possibly …
On Hopf algebras and the elimination theorem for free Lie algebras
自由李代数的消去定理是用自由李子代数描述自由李代数结构的一般原理，最近被E。Jurisich证明R. Borcherds的“怪物李代数”有某些大的自由李子代数，照亮了Borcherds的证明的一部分，即月光模顶点算子代数服从康威-诺顿定理。在本临时说明中，我们解释了如何消除定理有一个非常简单和自然的推广，并制定，霍普夫代数。这一事实已经从一般结果包含在未发表的1972年的工作，未知的我们，当我们写这篇文章，R。Block和P. Leroux。
Some twisted sectors for the Moonshine Module
对于其自同构是怪物${\Bbb M},$的月光模块$V^{\natural},$我们展示了如何为${\Bbb M}.$中的$2A,$ $2B$和$4A$类型的元素给出不可约$g$ -扭曲模块的一致存在性证明其中最有趣的是扭曲扇区$V^{\natural}(2A),$，其自同构群本质上是${\Bbb M}.$中$2A$的中心化子这是Baby Monster的2倍中心扩展，第二大散生单性类群。我们还建立了扭曲部门的唯一性和Hauptmodul性质的分次迹的自同构的奇数阶，预测的共形场论。
The Order of the Monster Finite Simple Group
本文通过基于Griess代数轴幂等元计数的计算方法，借助mmgroup软件完成了首个自包含的魔群阶计算，还证明了魔群的自同构群性质、对合共轭类数量并确定了小魔群的阶。
We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series of simple Lie groups and some exceptional finite simple groups including the Monster and Baby Monster.
Moonshine Cohomology
构造了一类新的从{ \it量子算子代数}到{ \it Batalin-Vilkovisky代数}的上同调函子.这个{ \it Moonshine上同调}作为一个自然自同构群，具有Fischer-Griess Monster有限群。我们证明了这个上同调的一般消失定理。对于一个二阶双曲格上的交换QOA，我们证明了一阶上同调同构于所谓的物理态李代数。在秩为2的幺模格的情形下，一次上同调给出了Borcherd Monster李代数的一个新的构造。作为应用，我们计算了由双曲格分次的厄米李代数的分次维数和上同调的签名。在本文的前半部分，我们对量子算子代数理论作了一个初步的阐述。一些结果在这里宣布讲座的第一作者在研究所数学科学在京都9月94日。
We propose that Borcherds' Fake Monster Lie algebra is a broken symmetry of heterotic string theory compactified on $T^7 \times T^2$. As evidence, we study the fully flavored counting function for BPS instantons contributing to a certain loop amplitude. The result is controlled by $Φ_{12}$, an automorphic form for $O(2, 26, \mathbb{Z})$. The degeneracies it encodes in its Fourier coefficients are graded dimensions of a second-quantized Fock space for this large symmetry algebra. This construction provides a concrete realization of Harvey and Moore's proposed relationship between Generalized Ka…
From vertex operator superalgebras to graded-local conformal nets and back
通过引入强分级局部顶点算子超代数概念，将顶点算子代数与共形网的对应推广至超代数情形，并证明了格VOSA、超Moonshine VOSA及短Moonshine VOSA的强分级局部性。
We discuss the classification of strongly regular vertex operator algebras (VOAs) with exactly three simple modules whose character vector satisfies a monic modular linear differential equation with irreducible monodromy. Our Main Theorem provides a classification of all such VOAs in the form of one infinite family of affine VOAs, one individual affine algebra and two Virasoro algebras, together with a family of eleven exceptional character vectors and associated data that we call the $U$-series. We prove that there are at least $15$ VOAs in the $U$-series occurring as commutants in a Schellek…
We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a general procedure which associates to every strongly local vertex operator algebra V a conformal net A_V acting on the Hilbert space completion of V and prove that the isomorphism class of A_V does not depend on the choice of the scalar product on V. We show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。