Two-parameter deformation of loop algebras and superalgebras

Details Two-parameter deformation of loop algebras and superalgebras Two-parameter deformation of loop algebras and superalgebras

1997-12-11

arxiv.org/abs/q-alg/9712028v1

Mathematics

Quantum Algebra

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

Scientific paper

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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