Framed vertex operator algebras, codes and the moonshine module

Abstract

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1/2, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge 1/2 are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras.

Latex, 54 pages

References in corpus (4)

• Modular invariance of trace functions in orbifold theory
• Representation theory and tensor product theory for vertex operator algebras
• Compact automorphism groups of vertex operator algebras
• Representation theory of Code VOA and construction of VOAs

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• The Moonshine Anomaly
• Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25
• On the structure of framed vertex operator algebras and their pointwise frame stabilizers
• Building vertex algebras from parts
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• Tensor Decomposition, Parafermions, Level-Rank Duality, and Reciprocity Law for Vertex Operator Algebras
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• C_2 cofiniteness of vertex operator algebra V_L^+ when L is a rank one lattice
• Integral forms for tensor powers of the Virasoro vertex operator algebra $L(\frac{1}{2},0)$ and their modules
• Rationality of vertex operator algebras
• Conformal Designs based on Vertex Operator Algebras
• Super-moonshine for Conway's largest sporadic group
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• The Group of Symmetries of the shorter Moonshine Module
• Associative subalgebras of low-dimensional Majorana algebras
• Classification of extremal vertex operator algebras with two simple modules
• Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models
• The commutant of $L_{{\widehat{\mathfrak{sl}}}_2}(n,0)$ in the vertex operator algebra $L_{{\widehat{\mathfrak{sl}}}_2}(1,0{)}^{\otimes n}$
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• Quantum Dimensions and Quantum Galois Theory
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• Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices
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• From Operator Algebras to Superconformal Field Theory
• Vertex operator algebras associated to the Virasoro algebra over an arbitrary field
• "McKay's E7 observation on the Baby Monster" and "McKay's E6 observation on the largest Fischer group"
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• Miyamoto groups of code algebras
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• Self-dual Codes over the Kleinian Four Group
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• Commutative algebras in Grothendieck-Verdier categories, rigidity, and vertex operator algebras
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• Bimodules associated to vertex operator algebras
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• The rank two lattice type vertex operator algebras V_L^+ and their automorphism groups
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• Classification of irreducible modules for the vertex operator algebra V_L^+: General case
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• A new existence proof of the Monster by VOA theory