Deformation of the harmonic oscillator algebra associated with the Morse potential and su(2) algebra is derived using quantum analogue of anharmonic oscillator. A change of parametrization leads naturally to Lie-algebraic approximations of the general q-deformation and physical interpretation of the deformation parameters. New algebraic realization of q-bosons is presented, q=root of unity, which corresponding to a periodic structure described by a finite-dimensional representation. It represents the symmetry of a linear lattice with periodic boundary conditions, providing a useful framework for deformation of crystalline and polymer Hamiltonians. Collaborative work with National Univ. of Mexico and Bulgaria Academy of Sci.