Two-parameter deformation of loop algebras and superalgebras
Tolstoy, Valeriy N.
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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=sl₂) is a twisting of the usual Yangian Yη(sl₂).
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