Noncommutative Differential Calculus: Quantum Groups, Stochastic   Processes, and the Antibracket
  We explore a differential calculus on the algebra of smooth functions on a manifold. The former is `noncommutative' in the sense that functions and differentials do not commute, in general. Relations with bicovariant differential calculus on certain quantum groups and stochastic calculus are discussed. A similar differential calculus on a superspace is shown to be related to the Batalin-Vilkovisky antifield formalism. 
A. Dimakis and F. M"uller-Hoissen