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Using the idea of shape invariance with respect to the main
quantum number \emph{n}, we represent Lie algebras u(2) and
u(1,1). The induced metric by the Casimir operator of Lie algebras
u(2) and u(1,1) leads us to obtain new solutions of the Dirac
equation corresponding to a $spin^{-\frac{1}{2}}$ charged particle
on the 2D sphere $S^{2}$ and the hyperbolic plane $H^{2}$ in the
presence of a magnetic monopole. It is shown that the related new
spinors represent the supersymmetry algebra, and that they satisfy
shape invariance equations with respect to \emph{n}.
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