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

Susumu Okubo
1998 Jingshin Theoretical Physics Symposium in Honor of Professor Ta-You Wu  
We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three. If we consider both spin 1 and 1/2 states, then the same method will lead to the Lie-super algebra osp(1,2). Also, the quantum generalization of the method is discussed on the basis of the quantum group $su_q(2)$.
doi:10.1142/9789812816566_0014 fatcat:ewd6subqkreyfbevbw7dgpxvom