THE NONLINEAR STRUCTURE ON THE GENERAL QUANTUM HYPERPLANES - THE QUANTUM HYPERSURFACES AND THE NONLINEAR REALIZATIONS OF THE QUANTUM GROUPS

In this paper we prove that by the use of an extended algebra the nonl inear transformations of the general quantum hyperplanes can be obtain ed. The images of this transformation and its linear part, which are t wo quantum hyperspaces, can be interpreted as a quantum hypersurface a nd its quantum tangent hyperplane, respectively. The quantum group con cerned is nonlinearly realized on this quantum hypersurface. The concr ete results of GL(q)(N), as an example, are calculated.