dorsal/arxiv
View SchemaTwo-parameter deformation of loop algebras and superalgebras
| Authors | Valeriy N. Tolstoy |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9712028 |
| URL | https://arxiv.org/abs/q-alg/9712028 |
Abstract
We discuss two-parameter deformations of an universal enveloping algebra $U(g[u])$ of a polynomial loop algebra $g[u]$, where $g$ is a finite-dimensional complex simple Lie algebra (or superalgebra). These deformations are Hopf algebras. One deformation called Drinfeldian is a quantization of $U(g[u])$ in the direction of a classical r-matrix which is a sum of the simplest rational and trigonometric r-matrices. Another deformation (discussed only for the case $g=sl_{2}$) is a twisting of the usual Yangian $Y_{\eta}(sl_{2})$.
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"abstract": "We discuss two-parameter deformations of an universal enveloping algebra\n$U(g[u])$ of a polynomial loop algebra $g[u]$, where $g$ is a\nfinite-dimensional complex simple Lie algebra (or superalgebra). These\ndeformations are Hopf algebras. One deformation called Drinfeldian is a\nquantization of $U(g[u])$ in the direction of a classical r-matrix which is a\nsum of the simplest rational and trigonometric r-matrices. Another deformation\n(discussed only for the case $g=sl_{2}$) is a twisting of the usual Yangian\n$Y_{\\eta}(sl_{2})$.",
"arxiv_id": "q-alg/9712028",
"authors": [
"Valeriy N. Tolstoy"
],
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"q-alg",
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"title": "Two-parameter deformation of loop algebras and superalgebras",
"url": "https://arxiv.org/abs/q-alg/9712028"
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