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arXiv · 1701.07846

Fricke Lie algebras and the genus zero property in Moonshine

Scott Carnahan
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Abstract

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.

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BibTeXRIS

Scott Carnahan. 2017-07-10. Fricke Lie algebras and the genus zero property in Moonshine. https://doi.org/10.1088/1751-8121%2Faa781d

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