| Jordanian Quantum Algebra ${\\cal U}_{\\sf h}(sl(N))$ via Contraction Method and Mapping (2005) | |||||||||||||||
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. | |||||||||||||||
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