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The universal R-matrix and its associated quantum algebra as functionals of the classical r-matrix: the $sl_{2}$ case

Laurent Freidel·J. M. Maillet
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Abstract

Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ and its universal quantum $R$-matrix are explicitely constructed as functionals of the associated classical $r$-matrix. In this framework, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ is naturally imbedded in the universal envelopping algebra of the $sl_{2}$ current algebra.

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Laurent Freidel, J. M. Maillet. 1992-10-07. The universal R-matrix and its associated quantum algebra as functionals of the classical r-matrix: the $sl_{2}$ case. https://doi.org/10.1016/0370-2693(92)91331-3

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