  We plan to translate the successful description of three-dimensional gravity
as a gauge theory in the noncommutative framework, making use of the covariant
coordinates. We consider two specific three-dimensional fuzzy spaces based on
SU(2) and SU(1,1), which carry appropriate symmetry groups. These are the
groups we are going to gauge in order to result with the transformations of the
gauge fields (dreibein, spin connection and two extra Maxwell fields due to
noncommutativity), their corresponding curvatures and eventually determine the
action and the equations of motion. Finally, we verify their connection to
three-dimensional gravity.
