Coloured Hopf algebras and their duals

Abstract

Coloured Hopf algebras, related to the coloured Yang-Baxter equation, are reviewed, as well as their duals. The special case of coloured quantum universal enveloping algebras provides a coloured extension of Drinfeld and Jimbo formalism. The universal $\cal T$-matrix is then generalized to the coloured context, and shown to lead to an algebraic formulation of the coloured RTT-relations, previously proposed by Basu-Mallick as part of a coloured extension of Faddeev, Reshetikhin, and Takhtajan approach to quantum groups and quantum algebras.