On a class of nonstandard quantum algebras and their representations

The nonstandard U(z)sl(2,IR) quantum algebra is considered together with other nonstandard algebras sharing the same universal R-matrix as well as a fixed Hopf subalgebra. Some boson realizations for these nonstandard algebras are obtained which are later used in order to compute in a simplified way their (finite and infinite dimensional) representations. In the limit when the deformation parameter z vanishes these realizations turn into the well known (one or two-boson) Gelfand-Dyson realizations for the corresponding classical Lie algebras.