Jordanian Quantum Algebra ${\mathcal{U}}_{\mathsf{h}}(sl(N))$ 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 ${\mathcal{U}}_{\mathsf{h}}(sl(3))$ which has a remarkably simple coalgebraic structure and contains the Jordanian Hopf algebra ${\mathcal{U}}_{\mathsf{h}}(sl(2))$, obtained by Ohn, as a subalgebra. A nonlinear map between ${\mathcal{U}}_{\mathsf{h}}(sl(3))$ and the classical $sl(3)$ algebra is then established. In the second part, we give the higher dimensional Jordanian algebras ${\mathcal{U}}_{\mathsf{h}}(sl(N))$ for all $N$. The Universal ${\mathcal{R}}_{\mathsf{h}}$-matrix of ${\mathcal{U}}_{\mathsf{h}}(sl(N))$ is also given.

17 pages, Latex

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