Compatible Poisson-Lie structures on the loop group of $SL_{2}$

Details Compatible Poisson-Lie structures on the loop group of $SL_{2}$ Compatible Poisson-Lie structures on the loop group of $SL_{2}$

1995-12-08

arxiv.org/abs/q-alg/9512011v1

Mathematics

Quantum Algebra

5 pages, amstex, no figures

Scientific paper

10.1007/BF01815525

We define a 1-parameter family of $r$-matrices on the loop algebra of
$sl_{2}$, defining compatible Poisson structures on the associated loop group,
which degenerate into the rational and trigonometric structures, and study the
Manin triples associated to them.

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