  We extend the Galilei group of space-time transformations by gradation,
construct interacting field-theoretic representations of this algebra, and show
that non-relativistic Super-Chern-Simons theory is a special case. We also
study the generalization to matrix valued fields, which are relevant to the
formulation of superstring theory as a $1/N_c$ expansion of a field theory. We
find that in the matrix case, the field theory is much more restricted by the
supersymmetry.
