Laplacian on fuzzy de Sitter space

We study details of geometry noncommutative de Sitter space: we determine the Riemann and Ricci curvature tensors, energy Laplacian. find, in particular, that fuzzy space is an Einstein space, $R_{ab}=-3\zeta\,\eta_{ab}$. The Laplacian, defined frame formalism, not hermitian gives nonunitary evolution. When symmetrically ordered, it has usual quadratic form $\Delta=\Pi_a\Pi^a$ (when acting on functions representation $\Psi\in {\cal H}$): find its eigenstates discuss spectrum. This result a first step scalar field $\Delta = [\Pi_a, [\Pi^a,\ ]]$, propagator.