Nonspherical Giant Gravitons and Matrix Theory

We consider the plane wave limit of the nonspherical giant gravitons. We compute the Poisson brackets of the coordinate functions and find a nonlinear algebra. We show that this algebra solves the supersymmetry conditions of the matrix model. This is the generalization of the algebraic realization of the spherical membrane as the “fuzzy sphere”. We describe finite dimensional representations of the algebra corresponding to the fuzzy torus. On leave from the Institute of Theoretical and Experimental Physics, 117259, Bol. Cheremushkinskaya, 25, Moscow, Russia.