Deformation of Yangian $Y(sl_2)$

TL;DR

This paper explicitly constructs a two-parameter quantum deformation of the Yangian for sl_2, introducing a new algebraic structure with a pseudotriangular form, quantum double, and RTT realization.

Contribution

It provides an explicit quantization of a non-standard rational solution of CYBE for sl_2 using twisting, resulting in a novel two-parameter deformed Yangian.

Findings

Explicit construction of the deformed Yangian $Y_{\eta,\xi}(sl_2)$

Development of the pseudotriangular structure and quantum double

Derivation of the universal R-matrix and RTT-realization

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 $Y_{\eta,\xi}(sl_2))$ 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 $Y_{\eta,\xi}(sl_2)$.