In this paper we report on the formulation of the non-commutative Chern-Simons (CS) theory where the spatial slice, an infinite strip, is a manifold with boundaries. Our approach involves the formulation of a new finite-dimensional matrix model which approximates the CS theory on the non-commmutative strip. This model has a fuzzy edge which becomes the required sharp edge when size of the matrices approaches infinity. The non-commutative CS theory on the strip is denned by this limiting procedure. The canonical analysis of the matrix theory reveals that there are edge observables in the theory generating a Lie algebra with properties similar to that of a non-abelian Kac-Moody algebra. Using some of the results of this analysis we discuss in detail the limit where this matrix model approximates the CS theory on the infinite strip.
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