Euclidean and super euclidean algebras and localizations of U_q (sl(2)) and U_q(osp(1j2))₁

In Ref. 1 we described homomorphisms of U_q((2)) and U((2)) into localizations of U((2)) and U_q((2)), respectively, with U((2)) being the universal enveloping algebra of the Lie algebra of SO(2) × _sT² the Euclidean group in the plane, with T² denoting translations of the plane and × _s semidirect product. In particular, we obtained explicit expressions for the generators of U _q((2)) and U((2)), respectively as irrational functions of U((2)) and U_q((2)). Herewith we further develop our results extending them to U_q((1|2)) and U ) with being the super Euclidean algebra.