Noncommutative geometry and a class of completely integrable models
  We introduce a Hodge operator in a framework of noncommutative geometry. The complete integrability of 2-dimensional classical harmonic maps into groups (sigma-models or principal chiral models) is then extended to a class of 'noncommutative' harmonic maps into matrix algebras. 
A. Dimakis and F. Muller-Hoissen