dorsal/arxiv
View SchemaDeformation of Yangian $Y(sl_2)$
| Authors | S. M. Khoroshkin, A. A. Stolin, V. N. Tolstoy |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9511005 |
| URL | https://arxiv.org/abs/q-alg/9511005 |
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 $Y_{\eta,\xi}(sl_2)$.
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"date_created": "2026-03-02T18:01:24.761000Z",
"date_modified": "2026-03-02T18:01:24.761000Z",
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"abstract": "A quantization of a non-standard rational solution of CYBE for $sl_2$ is\ngiven explicitly. We obtain the quantization with the help of a twisting of the\nusual Yangian $Y(sl_2$. This quantum object (deformed Yangian\n$Y_{\\eta,\\xi}(sl_2))$ is a two-parametric deformation of the universal\nenveloping algebra $U(sl_2[u])$ of the positive current algebra $sl_2[u]$. We\nconsider the pseudotriangular structure on $Y_{\\eta,\\xi}(sl_2)$, the quantum\ndouble $DY_{\\eta,\\xi}(sl_2)$ its the universal R-matrix and also the\nRTT-realization of $Y_{\\eta,\\xi}(sl_2)$.",
"arxiv_id": "q-alg/9511005",
"authors": [
"S. M. Khoroshkin",
"A. A. Stolin",
"V. N. Tolstoy"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Deformation of Yangian $Y(sl_2)$",
"url": "https://arxiv.org/abs/q-alg/9511005"
},
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"source": {
"execution_id": "20cf8075-7180-4379-a394-7866ded70eea",
"id": "arXiv Dataset IDs",
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"variant": "snapshot-2026-03-01",
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