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Monster vertex algebra

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The monster vertex algebra (or moonshine module) is a vertex algebra acted on by the monster group that was constructed by Igor Frenkel, James Lepowsky, and Arne Meurman. R. Borcherds used it to prove the monstrous moonshine conjectures, by applying the Goddard–Thorn theorem of string theory to construct the monster Lie algebra, an infinite-dimensional generalized Kac–Moody algebra acted on by the monster.