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The quantum mechanics of a spin $\frac{1}{2}$ particle on a
locally spatial constant curvature part of a $(2+1)$ -space?time
in the presence of a constant magnetic field of a magnetic
monopole has been investigated. It has been shown that these
two-dimensional Hamiltonians have the degeneracy group of
$SL(2,\emph{c})$, and para-supersymmetry of arbitrary order or
shape invariance. Using this symmetry we have obtained its
spectrum algebraically. The Dirac's quantization condition has
been obtained from the representation theory. Also, it is shown
that the presence of angular deficit suppresses both the
degeneracy and shape invariance.
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