Two-parameter deformation of loop algebras and superalgebras

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 $g=s{l}_2$) is a twisting of the usual Yangian $Y_{\eta }(s{l}_2)$.

Communication presented in the 5th Wigner Symposium, Vienna,1997; 3 pages, LaTeX