New r-Matrices for Lie Bialgebra Structures over Polynomials

Abstract

For a finite dimensional simple complex Lie algebra $${\mathfrak{g}}$$ , Lie bialgebra structures on $${\mathfrak{g}\left[\left[u \right]\right]}$$ and $${\mathfrak{g}\left[u\right]}$$ were classified by Montaner, Stolin and Zelmanov. In our paper, we provide an explicit algorithm to produce r-matrices which correspond to Lie bialgebra structures over polynomials.