Coloured FRT algebra and its Yang-Baxterization leading to integrable models with non-additive R-matrices

Abstract

A 'colour' representation of Faddeev-Reshetikhin-Takhtajan (FRT) algebra, which, in contrast to the standard case, is related to the coloured braid group representation with generic values of q is presented. Explicit realizations of L(+or-)-matrices, occurring in this coloured variant of FRT algebra, are also obtained for the Uq(gl(2)) quantized algebra. Though these realizations are found to depend manifestly on the colour parameters, the underlying quantum group structure and associated co-product are interestingly free from such dependence. This allows us to perform the Yang-Baxterization of the coloured FRT algebra successfully, which leads to the construction of an ancestor Law operator associated with a new non-additive-type quantum R-matrix. Through different realizations of this Lax operator, a new class of quantum integrable models representing 'colour' generalizations of the well known models, such as the lattice sine-Gordon model, the Ablowitz-Ladik model lattice and the derivative nonlinear Schrodinger model etc, is generated.