XXV Workshop on Geometric Methods in Physics 2-8.07.2006

Adrian Tanasa

Some solutions of the quantum Yang-Baxter equation

We present here an algorithm for obtaining a large family of solutions of the quantum Yang-Baxter equation. Starting from any vector space with a bilinear composition law we define some R-matrix. We then prove that this matrix is a solution of the constant Yang-Baxter equation. Note that the composition law considered may be chosed to be a Lie (super)bracket. Our approach thus establishes a direct connection between contraction parameters of the initial chosen Lie (super)algebra and the deformation parameters appering within the solutions of the Yang-Baxter equation.