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

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

2009-10-22

arxiv.org/abs/0910.4286v2

Mathematics

Quantum Algebra

Scientific paper

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.

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