  We build the Z$_{3}$ invariants fusion rules associated to the
(D$_{4}$,A$_{6}$) conformal algebra. This algebra is known to describe the
tri-critical Potts model. The 4-pt correlation functions of critical fields are
developed in the bootstrap approach, and in the other hand, they are written in
term of integral representation of the conformal blocks. By comparing both the
expressions, one can determine the structure constantes of the operator
algebra.
