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We give a new, simpler proof that the canonical actions of finite groups onFricke-type Monstrous Lie algebras yield genus zero functions in GeneralizedMonstrous Moonshine, using a Borcherds-Kac-Moody Lie algebra decomposition dueto Jurisich. We describe a compatibility condition, arising from the no-ghosttheorem in bosonic string theory, that yields the genus zero property. We giveevidence for and against the conjecture that such a compatibility forsymmetries of the Monster Lie algebra gives a characterization of the Monstergroup.

Fricke Lie algebras and the genus zero property in Moonshine