Binary Codes and Vertex Operator (Super)Algebras

Miyamoto, Masahiko

doi:10.1006/jabr.1996.0116

Cited by 61 publications

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“…To simplify the notation, we will omit superscripts [i] of M [i] from now on. We have proved the following theorem, whose complexification was proved in [Mi2].…”

Section: Code Voas With Pdib-formsmentioning

confidence: 90%

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A new construction of the moonshine vertex operator algebra over the real number field

Miyamoto

2004

Ann. Math.

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We give a new construction of the moonshine module vertex operator algebra V , which was originally constructed in [FLM2]. We construct it as a framed VOA over the real number field R. We also offer ways to transform a structure of framed VOA into another framed VOA. As applications, we study the five framed VOA structures on V E8 and construct many framed VOAs including V from a small VOA. One of the advantages of our construction is that we are able to construct V as a framed VOA with a positive definite invariant bilinear form and we can easily prove that Aut(V ) is the Monster simple group. By similar ways, we also construct an infinite series of holomorphic framed VOAs with finite full automorphism groups. At the end of the paper, we calculate the character of a 3C element of the Monster simple group.

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“…To simplify the notation, we will omit superscripts [i] of M [i] from now on. We have proved the following theorem, whose complexification was proved in [Mi2].…”

Section: Code Voas With Pdib-formsmentioning

confidence: 90%

“…Our main purpose in this paper is to reconstruct V as a framed VOA. Another important example of framed VOAs is a code VOA M D for an even linear code D, which is introduced by [Mi2]. It is known that every irreducible T -module W is a tensor product…”

Section: Introductionmentioning

confidence: 99%

A new construction of the moonshine vertex operator algebra over the real number field

Miyamoto

2004

Ann. Math.

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“…Then C also forms a binary code and V 0 = α∈C M α . The code VOA V C associated to a binary code C was defined in [Mi96]. Summarizing, there exists a pair of binary codes (C, D) such that…”

Section: Theorem 25 ([Dgh98])mentioning

confidence: 99%

Classification of holomorphic framed vertex operator algebras of central charge 24

Lam¹,

Shimakura²

2015

ajm

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Abstract. This article is a continuation of our work on the classification of holomorphic framed vertex operator algebras of central charge 24. We show that a holomorphic framed VOA of central charge 24 is uniquely determined by the Lie algebra structure of its weight one subspace. As a consequence, we completely classify all holomorphic framed vertex operator algebras of central charge 24 and show that there exist exactly 56 such vertex operator algebras, up to isomorphism.

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“…[13,19]). One advantage of their constructions is that it is easy to associate certain automorphisms to the VOA constructed (cf.…”

Section: Introductionmentioning

confidence: 97%

Z2×Z2 Codes and Vertex Operator Algebras

Lam

Yamada

2000

Journal of Algebra

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Binary Codes and Vertex Operator (Super)Algebras

Cited by 61 publications

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A new construction of the moonshine vertex operator algebra over the real number field

A new construction of the moonshine vertex operator algebra over the real number field

Classification of holomorphic framed vertex operator algebras of central charge 24

Z2×Z2 Codes and Vertex Operator Algebras

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