  Multiparameter quantum gl(N) is not a rigid structure. This paper defines an
essential deformation as one that cannot be interpreted in terms of a
similarity transformation, nor as a perturbation of the parameters. All the
equivalence classes of first order essential deformations are found, as well as
a class of exact deformations. This work provides quantization of all the
classical Lie bialgebra structures (constant r-matrices) found by Belavin and
Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a
cubic root of unity, stands out.
