Deformation of Yangian $Y(sl_2)$

S. M. Khoroshkin; A. A. Stolin; V. N. Tolstoy

paper

Deformation of Yangian $Y (s l_{2})$

arXiv:q-alg/9511005

Abstract

A quantization of a non-standard rational solution of CYBE for $s l_{2}$ is given explicitly. We obtain the quantization with the help of a twisting of the usual Yangian $Y (s l_{2}$ . This quantum object (deformed Yangian $Y_{η, ξ} (s l_{2}))$ is a two-parametric deformation of the universal enveloping algebra $U (s l_{2} [u])$ of the positive current algebra $s l_{2} [u]$ . We consider the pseudotriangular structure on $Y_{η, ξ} (s l_{2})$ , the quantum double $D Y_{η, ξ} (s l_{2})$ its the universal R-matrix and also the RTT-realization of $Y_{η, ξ} (s l_{2})$ .

13 pages, 44kb, LATEX

Deformation of Yangian Y(sl2​)

Abstract

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Deformation of Yangian $Y (s l_{2})$