R-matrices with gauge parameters and multi-parameter quantized enveloping algebras

Abstract

The authors introduce a multiparametric quantum deformation ofthe universal enveloping algebra of a symmetrizable Kac Moodyalgebra. Connections with earlier constructions of quantizedenveloping algebras are explicated. The exposition is brief andvery informative.\par The ideas of this paper parallel those of\Cite{Reshetikhin90:Multiparameter:331--335}[91k:17012]N.Reshetikhin [Lett. Math. Phys. 20 (1990), no. 4, 331 335; MR91k:17012], and 1182166 E. E. Demidov et al. [Progr. Theoret.Phys. Suppl. No. 102 (1990), 203 218 (1991)].\par {For theentire collection see MR 92m:33002.}