  We give a new, simpler proof that the canonical actions of finite groups on
Fricke-type Monstrous Lie algebras yield genus zero functions in Generalized
Monstrous Moonshine, using a Borcherds-Kac-Moody Lie algebra decomposition due
to Jurisich. We describe a compatibility condition, arising from the no-ghost
theorem in bosonic string theory, that yields the genus zero property. We give
evidence for and against the conjecture that such a compatibility for
symmetries of the Monster Lie algebra gives a characterization of the Monster
group.
