Vertex Operator Algebra
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, a framework that is essential to define string 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.
Important examples of vertex operator algebras include lattice VOAs (modeling lattice conformal field theories), VOAs given by representations of affine Kac-Moody algebras (from the WZW model), the Virasoro VOAs (i.e., VOAs corresponding to representations of the Virasoro algebra) and the moonshine module V♮, constructed by Frenkel, Lepowsky and Meurman in 1988.
Read more about Vertex Operator Algebra: Formal Definition, Symmetries, Motivation and Related Algebraic Structures, Alternative Definitions, Jacobi Identity, A Trivial Example, Heisenberg Lie Algebra Example, Virasoro Vertex Operator Algebra Example, Monster Vertex Algebra, Vertex Operator Superalgebra, Vertex Operator Algebra Defined By A Lattice
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