  The U(1) gauge theory on a space with Lie type noncommutativity is
constructed. The construction is based on the group of translation in Fourier
space, which in contrast to space itself is commutative. In analogy with
lattice gauge theory, the object playing the role of flux of field strength per
plaquette, as well as the action, are constructed. It is observed that the
theory, in comparison with ordinary U(1) gauge theory, has an extra gauge field
component. This phenomena is reminiscent of similar ones in formulation of
SU(N) gauge theory in space with canonical noncommutativity, and also
appearance of gauge field component in discrete direction of Connes'
construction of the Standard Model.
