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Deformation of Yangian $Y(sl_2)$

S. M. Khoroshkin·A. A. Stolin·V. N. Tolstoy
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Abstract

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 $Y_{η,ξ}(sl_2))$ 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 $Y_{η,ξ}(sl_2)$, the quantum double $DY_{η,ξ}(sl_2)$ its the universal R-matrix and also the RTT-realization of $Y_{η,ξ}(sl_2)$.

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BibTeXRIS

S. M. Khoroshkin, A. A. Stolin, V. N. Tolstoy. 1995-11-10. Deformation of Yangian $Y(sl_2)$. https://arxiv.org/abs/q-alg/9511005

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