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Theories with noncommutative space-time coordinates repr esent alternative candidates of grand unified theories. We discuss U(1) gauge theory in 2 and 4 dimen sions on a lattice with N sites. The mapping to a U(N) plaquette model in the sense of Eguchi and Ka wai can be used for computer simulations. In 2D it turns out that the formulation of the to pological charge leads to the imaginary part of the plaquette. Concerning 4D, the definition of insta tons seems straightforward. We show that one can transcribe the plaquette and hypercube formula tion to the matrix theory. It will be interesting to measure the topological charge on a noncommu tative hypercube.

Definition of Instantons in Noncommutative Gauge Theory in Higher Dimensions