Multiplicative integrable models from Poisson-Nijenhuis structures
arXiv:1507.01500 · doi:10.4064/bc106-0-2
Abstract
We discuss the role of Poisson-Nijenhuis 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 and studied in [arXiv:1503.07339].
21 pages. Based on the talk given at the conference "From Poisson Brackets to Universal Quantum Symmetries", August 18-22 2014, Stephan Banach International Mathematical Center, Warsaw