High Quality Content by WIKIPEDIA articles! In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in conformal field theory and related areas of physics. Vertex operator algebras have proven useful in purely mathematical contexts such as monstrous moonshine and the geometric Langlands correspondence.Vertex operator algebras were first introduced by Richard Borcherds in 1986, motivated by the vertex operators arising from field insertions in two dimensional conformal field theory. The axioms of a vertex operator algebra are a formal algebraic interpretation of what physicists called chiral algebras, whose definition was made mathematically rigorous by Alexander Beilinson and Vladimir Drinfel'd.

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