ABSTRACT
In this chapter, we introduce the noncommutative phase space functor Ph : Alg k → Alg k , defined for associative k-algebras, and the cosimplicial structure of the infinitely iterated phase space functor Ph*. We study the inductive limit Ph∞(A) of this cosimplicial object, and the induced universal derivation δ : Ph∞(A) → Ph∞(A), which is called the Dirac derivation. The corresponding relations to de Rham theory is treated in this general context.
