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/