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We will derive both quaternion and octonion algebras as the Clebsch-Gordanalgebras based upon the su(2) Lie algebra by considering angular momentumspaces of spin one and three. If we consider both spin 1 and 1/2 states, thenthe same method will lead to the Lie-super algebra osp(1,2). Also, the quantumgeneralization of the method is discussed on the basis of the quantum group$su_q(2)$.Comment: 17 pages, TE

ANGULAR MOMENTUM, QUATERNION, OCTONION, AND LIE-SUPER ALGEBRA OSP(1,2)