Integrable nonabelian systems are equations of motion in which the field variables take values in a nonabelian algebra, as a matrix one. As their classical counterparts, we can describe their structure and understand their integrability in terms of Poisson brackets, and introduce recursion (Nijenhuis) operators to derive the hierarchy from their biHamiltonian structure. I will describe some examples for differential-difference systems obtained in a joint work with J.P. Wang (Nonlinearity 2021) and propose a geometric interpretation of the Hamiltonian structure in terms of double algebras (preprint to be published in CMP).
