Integrability of characteristic Hamiltonian systems on simple Lie groups with standard Poisson Lie structure

TL;DR

This paper proves that characteristic Hamiltonian systems on simple Lie groups with standard Poisson Lie structures are always integrable, expanding understanding of their symplectic geometry and integrability properties.

Contribution

It demonstrates the universal integrability of characteristic Hamiltonian systems on simple Lie groups with standard Poisson Lie structures.

Findings

Characteristic Hamiltonian systems are always integrable.

Systems are defined on symplectic leaves of factorizable Poisson Lie groups.

Hamiltonians are conjugation-invariant functions.

Abstract

Phase space of a characteristic Hamiltonian system is a symplectic leaf of a factorizable Poisson Lie group. Its Hamiltonian is a restriction to the symplectic leaf of a function on the group which is invariant with respect to conjugations. It is shown in this paper that such system is always integrable.