Poisson-Lie Group structures on semidirect products
Quantum Algebra
2025-08-19 v2
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.
Cite
@article{arxiv.2203.14552,
title = {Poisson-Lie Group structures on semidirect products},
author = {Floris Elzinga and Makoto Yamashita},
journal= {arXiv preprint arXiv:2203.14552},
year = {2025}
}
Comments
18 pages, accepted version, minor changes; v1: 17 pages