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The quantum mechanics of a spin 1/2 particle on a locally spatial constantcurvature part of a (2+1)- spacetime in the presence of a constant magneticfield of a magnetic monopole has been investigated. It has been shown thatthese 2-dimensional Hamiltonians have the degeneracy group of SL(2,c), andpara-supersymmetry of arbitrary order or shape invariance. Using this symmetrywe have obtained its spectrum algebraically. The Dirac's quantization conditionhas been obtained from the representation theory. Also, it is shown that thepresence of angular deficit suppresses both the degeneracy and shapeinvariance.Comment: 31 pages, Latex, no figures, to be published in J. Math. Phy

Degeneracy and para-supersymmetry of Dirac Hamiltonian in (2+1)-space–time