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

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

2001-05-28

arxiv.org/abs/math/0105220v1

Mathematics

Quantum Algebra

17 pages, Latex

Scientific paper

10.1088/0305-4470/35/14/306

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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