Jordanian Quantum Algebra {\cal U}_{\sf h}(sl(N)) via Contraction Method and Mapping
Abstract
Using the contraction procedure introduced by us in Ref. \cite{ACC2}, we construct, in the first part of the present letter, the Jordanian quantum Hopf algebra {\cal U}_{\sf h}(sl(3)) which has a remarkably simple coalgebraic structure and contains the Jordanian Hopf algebra {\cal U}_{\sf h}(sl(2)), obtained by Ohn, as a subalgebra. A nonlinear map between {\cal U}_{\sf h}(sl(3)) and the classical sl(3) algebra is then established. In the second part, we give the higher dimensional Jordanian algebras {\cal U}_{\sf h}(sl(N)) for all N. The Universal {\cal R}_{\sf h}-matrix of {\cal U}_{\sf h} (sl(N)) is also given.