  We introduce an associative glueing operation $\oplus_q$ on the space of
solutions of the Quantum Yang-Baxter Equations of Hecke type. The corresponding
glueing operations for the associated quantum groups and quantum vector spaces
are also found. The former involves $2\times 2$ quantum matrices whose entries
are themselves square or rectangular quantum matrices. The corresponding
glueing operation for link-invariants is introduced and involves a state-sum
model with Boltzmann weights determined by the link invariants to be glued. The
standard $su(n)$ solution, its associated quantum matrix group, quantum space
and link-invariant arise at once by repeated glueing of the one-dimensional
case.
