  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.
