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arXiv · 2203.14552

Poisson-Lie Group structures on semidirect products

Floris Elzinga·Makoto Yamashita
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Abstract

We look at the Poisson structure on the total space of the dual bundle to the Lie algebroid arising from a matched pair of Lie groups. This dual bundle, with the natural semidirect product group structure, becomes a Poisson-Lie group as suggested by a recent work of Stachura. Moreover, when we start from matched pairs given by the Iwasawa decomposition of simple Lie groups, the associated Lie bialgebra is coboundary.

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Floris Elzinga, Makoto Yamashita. 2022-03-28. Poisson-Lie Group structures on semidirect products. https://doi.org/10.4171/jncg/538

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