Area preserving diffeomorphism, quantum group and Berry phase

We study here the relationship between the area preserving diffeomorphism a nd quantum group with the deformation of symplectic structure and Berry pha se in the Landau problem of 2D electron gas in a magnetic field. It is argu ed that while the area preserving diffeomorphism leads to the quantization of the symmetry U-q(SL(2)), the deformation of the symplectic structure lea ds to the quantization of the system having the relation ap. Delta q = 2 pi nh, n being an odd integer giving rise to the Berry phase e(i2 pi mu) with n = 2 mu. A possible link between the deformation parameter q of the defor med algebra U-q(SL(2)) with the Berry phase factor arising out of the quant ization procedure has been suggested. Finally, the latticization of space a ssociated with the quantum group and its connection with the Z(p) spin syst em is discussed.