Editing Vertex operator algebra (section)

=== Monster vertex algebra ===
The [[monster vertex algebra]] <math>V^\natural</math> (also called the "moonshine module") is the key to Borcherds's proof of the [[Monstrous moonshine]] conjectures. It was constructed by Frenkel, Lepowsky, and Meurman in 1988. It is notable because its character is the [[j-invariant]] with no constant term, <math>j(\tau) - 744</math>, and its automorphism group is the [[monster group]]. It is constructed by orbifolding the lattice vertex algebra constructed from the [[Leech lattice]] by the order 2 automorphism induced by reflecting the Leech lattice in the origin. That is, one forms the direct sum of the Leech lattice VOA with the twisted module, and takes the fixed points under an induced involution. Frenkel, Lepowsky, and Meurman conjectured in 1988 that <math>V^\natural</math> is the unique holomorphic vertex operator algebra with central charge 24, and partition function <math>j(\tau) - 744</math>. This conjecture is still open.