  The $q$-Poincar\'e group of \cite{SWW:inh} is shown to have the structure of
a semidirect product and coproduct $B\cocross \widetilde{SO_q(1,3)}$ where $B$
is a braided-quantum group structure on the $q$-Minkowski space of 4-momentum
with braided-coproduct $\und\Delta \vecp=\vecp\tens 1+1\tens \vecp$. Here the
necessary $B$ is not a usual kind of quantum group, but one with braid
statistics. Similar braided-vectors and covectors $V(R')$, $V^*(R')$ exist for
a general R-matrix. The abstract structure of the $q$-Lorentz group is also
studied.
