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arXiv · q-alg/9712028

Two-parameter deformation of loop algebras and superalgebras

Valeriy N. Tolstoy
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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 $Y_η(sl_{2})$.

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Valeriy N. Tolstoy. 1997-12-11. Two-parameter deformation of loop algebras and superalgebras. https://arxiv.org/abs/q-alg/9712028

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