MAPS AND TWISTS RELATING U(sl(2)) AND THE NONSTANDARD Uh(sl(2)): UNIFIED CONSTRUCTION

Abstract

A general construction is given for a class of invertible maps between the classical U ( sl (2)) and the Jordanian U h( sl (2)) algebras. Here the role of the maps is studied in the context of construction of twist operators relating the cocommutative and non-cocommutative coproducts of the U(sl(2)) and U h( sl (2)) algebras respectively. It is shown that a particular map called the "minimal twist map" implements the simplest twist given directly by the factorized form of the ℛh matrix of Ballesteros–Herranz. For a "non-minimal" map the twist has an additional factor obtainable in terms of the similarity transformation relating the map in question to the minimal one. Our general prescription may be used to evaluate the series expansion in powers of h of the twist operator corresponding to an arbitrary "non-minimal" map. The classical and the Jordanian antipode maps may also be interrelated by suitable similarity transformations.