DEFORMATIONS OF MULTIPARAMETER QUANTUM GL(N)

Multiparameter quantum gl(N) is not a rigid structure. This Letter def ines an essential deformation as one that cannot be interpreted in ter ms of a similarity transformation, nor as a perturbation of the parame ters. All the equivalence classes of first-order essential deformation s are found, as well as a class of exact deformations. This work provi des quantization of all the classical Lie bialgebra structures (consta nt 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, stand s out.