A SIMPLE METHOD FOR CONSTRUCTING THE INHOMOGENEOUS QUANTUM GROUP IGL(Q)(N) AND ITS UNIVERSAL ENVELOPING ALGEBRA U-Q(IGL(N))

We propose a simple and concise method to construct the inhomogeneous quantum group IGL(q)(n) and its universal enveloping algebra U-q(igl(n )). Our technique is based on embedding an n-dimensional quantum space in an n+1-dimensional one as the set x(n+1)=1. This is possible only if one considers the multiparametric quantum space whose parameters ar e fixed in a specific way. The quantum group IGL(q)(n) is then the sub set of GL(q)(n + 1), which leaves the x(n+1)=1 subset invariant. For t he deformed universal enveloping algebra U-q(igl(n)), we will show tha t it can also be embedded in U-q(gl(n+1)), provided one uses the multi parametric deformation of U(gl(n+1)) with a specific choice of its par ameters. (C) 1995 American Institute of Physics.