Abstract
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.
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