  The non-Abelian symmetries of the half-infinite XXZ spin chain for all
possible types of integrable boundary conditions are classified. For each type
of boundary conditions, an analog of the Chevalley-type presentation is given
for the corresponding symmetry algebra. In particular, two new algebras arise
that are, respectively, generated by the symmetry operators of the model with
triangular and special $U_q(gl_2)-$invariant integrable boundary conditions.
