Extending a result of Vassilevich, we obtain the asymptotic expansion for the trace of a spatially regularized heat operator , where is a generalized Laplacian defined with Moyal products and is Moyal left multiplication. The Moyal planes corresponding to any skewsymmetric matrix being spectral triples, the spectral action introduced in noncommutative geometry by Chamseddine and Connes is computed. This result generalizes the Connes–Lott action previously computed by Gayral for symplectic .
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