We discuss the role of Poisson-Nijenhuis (PN) geometry in the definition of multiplicative integrable models on symplectic groupoids. These are integrable models that are compatible with the groupoid structure in such a way that the set of contour levels of the hamiltonians in involution inherits a topological groupoid structure. We show that every maximal rank PN structure defines such a model. We consider the examples defined on compact hermitian symmetric spaces studied by F. Bonechi, J. Qiu and M. Tarlini (arXiv.org, 2015).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc106-0-2,
author = {Francesco Bonechi},
title = {Multiplicative integrable models from Poisson-Nijenhuis structures},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {19-33},
zbl = {1333.53121},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc106-0-2}
}
Francesco Bonechi. Multiplicative integrable models from Poisson-Nijenhuis structures. Banach Center Publications, Tome 104 (2015) pp. 19-33. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc106-0-2/