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.
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The definition of the vertex operators Φα(z) in this context is originally due to Victor Kac, Igor Frenkel and independently Graeme Segal.
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