Euclidean and super Euclidean algebras and Localizations of Uq((2)) and Uq((1|2))

Abstract

In Ref. 1 we described homomorphisms of Uq((2)) and U((2)) into localizations of U((2)) and Uq((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 Uq((2)) and U((2)), respectively as irrational functions of U((2)) and Uq((2)). Herewith we further develop our results extending them to Uq((1|2)) and U ) with being the super Euclidean algebra.