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

B. Enriquez; V. N. Rubtsov

doi:10.1007/bf01815525

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arXiv · q-alg/9512011

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

B. Enriquez·V. N. Rubtsov

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Abstract

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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BibTeX RIS

B. Enriquez, V. N. Rubtsov. 1995-12-08. Compatible Poisson-Lie structures on the loop group of $SL_{2}$. https://doi.org/10.1007/bf01815525

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