Department of Mathematics,
University of Wales Swansea,
Singleton Park, Swansea SA2 8PP,

Some new solutions to the one and two parameter forms of the quantum Yang-Baxter equation

The quantum Yang-Baxter equation (QYBE) has three fundamental forms: the constant, the one parameter, and the two parameter. Most of the known solutions to these come from examples of quasitriangular Hopf algebras. In a somewhat new approach, certain operators called Yang-Baxter (YB) operators arising from purely algebra structures turn out to be solutions of the constant QYBE. In this work, we investigate spectral-parameter dependent YB operators arising from algebra structures that solve the one and two parameter forms of the QYBE. We construct two families of such operators which are also connected to bialgebras through the FRT construction. Further, we also establish a link with YB systems.