A General Criterion of Quantum Integrability Accommodating Central   Charges and Anomalies
  A simple quantum generalisation of the Liouville-Arnold criterion of classical integrability is proposed: A system is quantum-integrable if it has an abelian Lie group of Wigner symmetries of dimension equal to the number of degrees of freedom. The criterion goes significantly beyond the familiar case of involutive conserved operators to cover systems with anomalies in which involutivity is modified by central charges. "Anomalous" quantum integrability is shown to have all the expected consequences including exact diagonalisability. The approach throws new light on the origin of Weyl group invariance. 
P.P.Divakaran