  The 2-dimensional space-time sine-Gordon field theory is extended
algebraically within the n-dimensional space of extended complex numbers. This
field theory is constructed in terms of an adapted extension of standard vertex
operators. A whole set of non-local conserved charges is constructed and
studied in this framework. Thereby, an algebraic non-perturbative description
is possible for this n-1 parameters family of quantum field theories. Known
results are obtained for specific values of the parameters, especially in
relation to affine Toda field theories. Different (dual)-models can then be
described in this formalism.
