Noncommutative differential calculi and the unifying zero curvature   representation of integrable systems
  Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based differential calculus. By means of this theory, we give out the zero-curvature representation of the continuum-continuum, discrete-continuum and discrete-discrete integrable systems in an unifying manner. 
Yongqiang Bai, Ming Pei and Huijuan Fu
math-ph math.MP