Abstract
A maximally supersymmetric configuration of super
Yang-Mills living on a non-commutative torus corresponds
to a constant curvature connection. On a non-commutative
toroidal orbifold there is an additional constraint that
the connection be equivariant. We study moduli spaces of
(equivariant) constant curvature connections on
non-commutative even-dimensional tori and on toroidal
orbifolds. As an illustration we work out the cases of
2 and 4 orbifolds in
detail. The results we obtain agree with a commutative
picture describing systems of branes wrapped on cycles
of the torus and branes stuck at exceptional orbifold
points.