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Vertex operator algebra

In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory. In addition to physical applications, vertex operator algebras have proven useful in purely mathematical contexts such as monstrous moonshine and the geometric Langlands correspondence.

Products, Examples from Lie algebras & Additional examples

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Overview

Basic properties

Examples from Lie algebras

Modules

Additional examples

Vertex operator superalgebras

Superconformal structures

Related algebraic structures

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Vertex operator algebra

Nodes119
Edges118
Triples105
Avg. degree1.98
Density0.016807
Components1

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Vertex operator algebra

Top relations

related to Additional constructions · 32
Vertex operator algebra → Again, An, And, Another, BRST, C2, Current, Drinfeld, Fixed, For, Given, Goddard, In, Ising, Kac, Kent, Lattice, Miyamoto, Moody, More
related to Related algebraic structures · 27
Vertex operator algebra → Any, Beilinson, Delta, Dong, Drinfeld, DX-module, Etingof, Frenkel, Given, If, Kac, Kazhdan, Lepowsky, Li, Lie, Moody, More, One, OPE, OPEs
related to Monster vertex algebra · 11
Vertex operator algebra → Borcherds's, Frenkel, It, Leech, Lepowsky, Meurman, Monstrous, That, The, This, VOA
related to Commutative vertex algebras · 7
Vertex operator algebra → Conversely, End, Given, Hence, If, This, Thus
related to Heisenberg vertex operator algebra · 7
Vertex operator algebra → Fock, Heisenberg, Heisenberg Lie, It, The, The Fock, V0
related to Virasoro vertex operator algebra · 7
Vertex operator algebra → First, If, In, Second, The, The Virasoro, Virasoro
related to Modules · 4
Vertex operator algebra → Hilbert, Modules, Much, That
is a · 3
Vertex operator algebra → pair of odd elements τ, unique simple quotient of the vacuum module of the affine Kac, vertex algebra equipped with a conformal element ω
related to Vertex operator algebra · 1
Vertex operator algebra → Virasoro

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Important terminology

vertex algebra displaystyle operator algebras one field conformal virasoro given vector lattice theory modules central space lie structure called operators

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Vertex operator algebrais avertex algebra equipped with a conformal element ω0.90text
Vertex operator algebrais aunique simple quotient of the vacuum module of the affine Kac0.90text
Vertex operator algebrais apair of odd elements τ0.90text
monstrous moonshineinstance ofvertex operator algebras have proven useful in purely mathematical contexts0.80text
the geometric Langlands correspondence.The related notion of vertex algebra was introduced by Richard Borcherds in 1986instance ofvertex operator algebras have proven useful in purely mathematical contexts0.80text
motivated by a construction of an infinite-dimensional Lie algebra due to Igor Frenkelinstance ofvertex operator algebras have proven useful in purely mathematical contexts0.80text
affine W-algebrasinstance ofMore sophisticated examples0.80text
the chiral de Rham complex on a complex manifold arise in geometric representation theoryinstance ofMore sophisticated examples0.80text
mathematical physicsinstance ofMore sophisticated examples0.80text
Vertex operator algebrarelated to Additional constructionsFixed0.60section
Vertex operator algebrarelated to Additional constructionsGiven0.60section
Vertex operator algebrarelated to Additional constructionsIn0.60section

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