On combined standard–nonstandard or hybrid (q,h)-deformations

Abstract

Combined (q,h)-deformations proposed by Kupershmidt and Ballesteros–Herranz–Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard q-deformation. We briefly indicate that appropriate singular limits of the same type of transformations can however lead from standard biparametric (p,q)-deformations to nonhybrid but biparametric nonstandard (g,h) ones. Finally a case of hybrid (q,h)-deformation is recalled, related to the superalgebra GL(1|1).