Výsledky vyhledávání - "Robert L. Griess"

Groups of Lie Type, Vertex Algebras, and Modular Moonshine

Publikováno v: International Mathematics Research Notices. 2015:10716-10755

We use recent work on integral forms in vertex operator algebras to construct vertex algebras over general commutative rings and Chevalley groups acting on them as vertex algebra automorphisms. In this way, we get series of vertex algebras over field

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https://doi.org/10.1093/imrn/rnv003

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Moonshine paths for 3 A and 6 A nodes of the extendedE8-diagram

Autor: Ching Hung Lam, Robert L. Griess

Publikováno v: Journal of Algebra. 379:85-112

We continue the program to make a moonshine path between a node of the extended E 8 -diagram and the Monster. Our theory is a concrete model expressing some of the mysterious connections identified by John McKay, George Glauberman and Simon Norton. I

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https://doi.org/10.1016/j.jalgebra.2012.12.019

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Moonshine paths and a VOA existence proof of the Monster

Autor: null Robert L. Griess Jr.

Publikováno v: Recent Developments in Lie Algebras, Groups and Representation Theory. :165-172

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::28aae45ff4c57fdbeba04625e6089a0c
https://doi.org/10.1090/pspum/086/1416

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Diagonal lattices and rootless EE8 pairs

Autor: Robert L. Griess, Ching Hung Lam

Publikováno v: Journal of Pure and Applied Algebra. 216:154-169

Let E be an integral lattice. We first discuss some general properties of an SDC lattice, i.e., a sum of two diagonal copies of E in E⊥E. In particular, we show that its group of isometries contains a wreath product. We then specialize this study t

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https://doi.org/10.1016/j.jpaa.2011.05.015

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A moonshine path for 5A and associated lattices of ranks 8 and 16

Autor: Robert L. Griess, Ching Hung Lam

Publikováno v: Journal of Algebra. 331(1):338-361

We continue the program, begun in Griess and Lam (in press) [18] , to make a moonshine path between a node of the extended E 8 -diagram and the Monster. Our goal is to provide a context for observations of McKay, Glauberman and Norton by realizing th

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EE8-Lattices and Dihedral Groups

Autor: Ching Hung Lam, Robert L. Griess

Publikováno v: Pure and Applied Mathematics Quarterly. 7:621-744

We classify integral rootless lattices which are sums of pairs of EE8-lattices (lattices isometric to √ 2 times the E8-lattice) and which define dihedral groups of orders less than or equal to 12. Most of these may be seen in the Leech lattice. Our

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https://doi.org/10.4310/pamq.2011.v7.n3.a6

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Rank 72 high minimum norm lattices

Autor: Robert L. Griess

Publikováno v: Journal of Number Theory. 130(7):1512-1519

Given a polarization of an even unimodular lattice and integer $k\ge 1$, we define a family of unimodular lattices $L(M,N,k)$. Of special interest are certain $L(M,N,3)$ of rank 72. Their minimum norms lie in $\{4, 6, 8\}$. Norms 4 and 6 do occur. Co

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