  This paper studied what shall be called the Long equation: that is the system
of nonlinear equation $R^{12}R^{13}=R^{13}R^{12}$ and $R^{12}R^{23}=
R^{23}R^{12}$. Any solution of this system supplies us a solution for the
integrability solution of Knizhnic-Zamolodchikov equation. We shall approach
this equation by introducing a new class of bialgebras, which we call Long
bialgebras. A FRT type theorem is given: in the finite case any solution of the
above equation is a co-homotety where the vector spase is a comodule over a
Long bialgebra.
