  The algebraic structure underlying the classical $r$-matrix formulation of
the complex sine-Gordon model is fully elucidated. It is characterized by two
matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a
modified classical reflection/Yang--Baxter set of equations, further deformed
by non-abelian dynamical shift terms along the dual Lie algebra $su(2)^*$. The
sign shift pattern of this deformation has the signature of the twisted
boundary dynamical algebra. Issues related to the quantization of this
algebraic structure and the formulation of quantum complex sine-Gordon on those
lines are introduced and discussed.
