Abstract
Two explicit q-deformations each of SU(2) and SU(1,1) algebras are constructed by simply imposing the condition of obtaining the limiting classical algebras. No explicit transformations of the generators are used. One construction results in the standard SU q(2) and SU q(1,1) algebras with q-deforming functionals as infinite odd power series of both J3 and the deformation parameter q. The other construction (also with q-deforming functionals as infinite power series) seems to be new, with additional free parameters in both the algebras and Casimirs.
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