Deformation of Yangian $Y(sl_2)$

Details Deformation of Yangian $Y(sl_2)$ Deformation of Yangian $Y(sl_2)$

1995-11-10

arxiv.org/abs/q-alg/9511005v1

Mathematics

Quantum Algebra

13 pages, 44kb, LATEX

Scientific paper

A quantization of a non-standard rational solution of CYBE for $sl_2$ is given explicitly. We obtain the quantization with the help of a twisting of the usual Yangian $Y(sl_2$. This quantum object (deformed Yangian $Y_{\eta,\xi}(sl_2))$ is a two-parametric deformation of the universal enveloping algebra $U(sl_2[u])$ of the positive current algebra $sl_2[u]$. We consider the pseudotriangular structure on $Y_{\eta,\xi}(sl_2)$, the quantum double $DY_{\eta,\xi}(sl_2)$ its the universal R-matrix and also the RTT-realization of $Y_{\eta,\xi}(sl_2)$.

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