Quantum groups of Lie colour algebras fulfilling the Cartan-Weyl paradigm

Abstract

Let Gamma be an additive abelian group with a commutative factor omega. We describe the simple and untwisted affine Lie colour algebras which admit a Cartan - Weyl description. For both classes, we construct the quantised universal enveloping colour algebras, and establish their quasi-triangular Hopf colour algebraic structure. These colour quantum groups generalise the Drinfeld - Jimbo quantum groups, which are recovered when Gamma is trivial. They provide an algebraic foundation for investigations in knot theory and soluble models in statistical mechanics.

Editing of Introduction, Inclusion of list of notations and a Conclusion; Final version to appear in J Geometry Physics; 81 pages