  We construct 2 families of automorphic forms related to twisted fake monster
algebras and calculate their Fourier expansions. This gives a new proof of
their denominator identities and shows that they define automorphic forms of
singular weight. We also obtain new infinite product identities which are the
denominator identities of generalized Kac-Moody superalgebras. Finally we
describe the reflection groups of the root lattices of these algebras.
