  We study aspects of the theory of generalized Kac-Moody Lie algebras (or
Borcherds algebras) and their standard modules. It is shown how such an algebra
with no mutually orthogonal imaginary simple roots, including Borcherds'
Monster Lie algebra $\frak m$, can be naturally constructed from a certain
Kac-Moody subalgebra and a module for it. We observe that certain generalized
Verma (induced) modules for generalized Kac-Moody algebras are standard modules
and hence irreducible. In particular, starting from the moonshine module for
the Monster group $M$, we construct a certain $\{frak gl}_2$- and $M$-module,
the tensor algebra over which carries a natural structure of irreducible module
for $\frak m$, which is realized as an explicitly prescribed $M$-covariant Lie
algebra of operators on this tensor algebra. The existence of large free
subalgebras of $\frak m$ is further exploited to provide a simplification of
Borcherds' proof of the Conway-Norton conjectures for the McKay-Thompson series
of the moonshine module. The coefficients of these series are shown to satisfy
natural recursion relations (replication formulas) equivalent to, but different
from, those obtained by Borcherds.
