  In this work we demonstrate new BCH-like relations involving the generators
of the su(1, 1), su(2) and so(2, 1) Lie algebras. We use our results to obtain
in a straightforward way the composition of an arbitrary number of elements of
the corresponding Lie groups. In order to make a self-consistent check of our
results, as a first application we recover the non-trivial composition law of
two arbitrary squeezing operators. As a second application, we show how our
results can be used to compute the time evolution operator of physical systems
described by time-dependent hamiltonians given by linear combinations of the
generators of the aforementioned Lie algebras.
