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We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory toa zero-dimensional 3-Lie algebra model and construct various stable solutionscorresponding to quantized Nambu-Poisson manifolds. A recently proposed Higgsmechanism reduces this model to the IKKT matrix model. We find that in thestrong coupling limit, our solutions correspond to ordinary noncommutativespaces arising as stable solutions in the IKKT model with D-brane backgrounds.In particular, this happens for S^3, R^3 and five-dimensional Neveu-SchwarzHpp-waves. We expand our model around these backgrounds and find effectivenoncommutative field theories with complicated interactions involvinghigher-derivative terms. We also describe the relation of our reduced model toa cubic supermatrix model based on an osp(1|32) supersymmetry algebra.

Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model