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Vertex operator algebraInmathematics, avertex operator algebra(VOA) is an algebraic structure that plays an important role inconformal field theoryandstring theory. In addition to physical applications, vertex operator algebras have proven useful in purely mathematical contexts such asmonstrous moonshineand thegeometric Langlands correspondence.The related notion ofvertex algebrawas introduced byRichard Borcherdsin 1986, motivated by a construction of an infinite-dimensional Lie algebra due toFrenkel. In the course of this construction, one employs aFock spacethat admits an action of vertex operators attached to lattice vectors. Borcherds formulated the notion of vertex algebra by axiomatizing the relations between the lattice vertex operators, producing an algebraic structure that allows one to construct new Lie algebras by following Frenkel's method

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