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.