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 nonlinear transformations of the general quantum hyperplanes can be obtained. The images of this transformation and its linear part, which are two quantum hyperspaces, can be interpreted as a quantum hypersurface and its quantum tangent hyperplane, respectively. The quantum group concerned is nonlinearly realized on this quantum hypersurface. The concrete results of GL(q)(N), as an example, are calculated.