Quantum deformations of SU(2)

Explicit representations of two deformations of SU(2), one in the Cartan basis, and one in the Cartesian basis, are constructed. The Cartan deformation subsumes previously known cases, while the Cartesian deformation appears to be new. In the latter case, explicit reversible mappings in terms of representations of SU(2) and a Casimir for the algebra are constructed.