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

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

1992-10-07

arxiv.org/abs/hep-th/9210039v1

Phys.Lett. B296 (1992) 353-360

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

10.1016/0370-2693(92)91331-3

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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