  In this paper we consider a connection between the Moyal formuration of
quantum mechanics and noncommutative lattices on nonlocal spaces. The Moyal
bracket generates SU(N) Lie algebras,and representations of these algebras
correspond to Bratteli diagrams on Hilbert spaces of C*-algebras, and also
representations of noncommutative lattices on nonlocal spaces correspond to the
same diagrams. We will show that the quantization thus generates nonlocal
spaces by the intermediation of Bratteli diagrams.The above connection are
investigated in details in two definite cases, one is one-dimensional lattice
QCD SU(N) fields on the unit circle, the other is Penrose lattice SU-type Lie
algebra fields on the Penrose lattice.
