Title: BPS Algebras, Genus Zero, and the Heterotic Monster,
Abstract: In this note, we expand on some technical issues raised in \cite{PPV} by the
authors, as well as providing a friendly introduction to and summary of our
previous work. We construct a set of heterotic string compactifications to 0+1
dimensions intimately related to the Monstrous moonshine module of Frenkel,
Lepowsky, and Meurman (and orbifolds thereof). Using this model, we review our
physical interpretation of the genus zero property of Monstrous moonshine.
Furthermore, we show that the space of (second-quantized) BPS-states forms a
module over the Monstrous Lie algebras $\mathfrak{m}_g$---some of the first and
most prominent examples of Generalized Kac-Moody algebras---constructed by
Borcherds and Carnahan. In particular, we clarify the structure of the module
present in the second-quantized string theory. We also sketch a proof of our
methods in the language of vertex operator algebras, for the interested
mathematician.