Deformation of Yangian $Y(sl_2)$

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 $Y_{η,ξ}(sl_2)$.