English

Two-parameter deformation of loop algebras and superalgebras

q-alg 2007-05-23 v1 Quantum Algebra

Abstract

We discuss two-parameter deformations of an universal enveloping algebra U(g[u])U(g[u]) of a polynomial loop algebra g[u]g[u], where gg 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])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=sl2g=sl_{2}) is a twisting of the usual Yangian Yη(sl2)Y_{\eta}(sl_{2}).

Keywords

Cite

@article{arxiv.q-alg/9712028,
  title  = {Two-parameter deformation of loop algebras and superalgebras},
  author = {Valeriy N. Tolstoy},
  journal= {arXiv preprint arXiv:q-alg/9712028},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T19:22:23.265Z