New $r$-Matrices for Lie Bialgebra Structures over Polynomials

Abstract

For a finite dimensional simple complex Lie algebra $\mathfrak{g}$, Lie bialgebra structures on $\mathfrak{g}[[u]]$ and $\mathfrak{g}[u]$ 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.

References in corpus (4)

• On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization
• The 4(th) structure
• Classical dynamical r-matrices, Poisson homogeneous spaces, and Lagrangian subalgebras
• A link between two elliptic quantum groups

Cited by in corpus (2)

• On the General Classification of Lie Bialgebra Structures over Polynomials
• Classification of Lie bialgebras over current algebras