  We give a framework to describe gauge theory on a certain class of
commutative but non-associative fuzzy spaces. Our description is in terms of an
Abelian gauge connection valued in the algebra of functions on the cotangent
bundle of the fuzzy space. The structure of such a gauge theory has many formal
similarities with that of Yang-Mills theory. The components of the gauge
connection are functions on the fuzzy space which transform in higher spin
representations of the Lorentz group. In component form, the gauge theory
describes an interacting theory of higher spin fields, which remains
non-trivial in the limit where the fuzzy space becomes associative. In this
limit, the theory can be viewed as a projection of an ordinary non-commutative
Yang-Mills theory. We describe the embedding of Maxwell theory in this extended
framework which follows the standard unfolding procedure for higher spin gauge
theories.
