The Chern-Simons one-form and gravity on a fuzzy space

The one-dimensional N×N-matrix Chern-Simons action is given, for large N and for slowly varying fields, by the (2k+1)-dimensional Chern-Simons action SCS, where the gauge fields in SCS parametrize the different ways in which the large N limit can be taken. Since some of these gauge fields correspond to the isometries of the space, we argue that gravity on fuzzy spaces can be described by the one-dimensional matrix Chern-Simons action at finite N and by the higher dimensional Chern-Simons action when the fuzzy space is approximated by a continuous manifold.