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Generalized Moonshine IV: Monstrous Lie algebras
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For each element of the Fischer-Griess Monster sporadic simple group, we construct an infinite dimensional Lie algebra equipped with a projective action of the centralizer of that element. Our construction is given by a string-theoretic "add a spacetime torus and quantize" functor applied to an abelian intertwining algebra that is formed from a family of twisted modules of the Monster vertex operator algebra. We prove that for all Fricke elements in the Monster, the characters of centralizers acting on the corresponding irreducible twisted modules are Hauptmoduln. From these results, we resolve Norton's Generalized Moonshine Conjecture.
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Vertex algebras, topological defects, and Moonshine
Duality defects in the Monster module have an explicit McKay-Thompson formula, and Conway-module defects preserving the N=1 superconformal algebra induce Leech-lattice endomorphisms.
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