  Using Noether's procedure we present a complete solution for the trilinear
interactions of arbitrary spins $s_{1},s_{2}, s_{3}$ in a flat background, and
discuss the possibility to enlarge this construction to higher order
interactions in the gauge field. Some classification theorems of the cubic
(self)interaction with different numbers of derivatives and depending on
relations between the spins are presented. Finally the expansion of a general
spin $s$ gauge transformation into powers of the field and the related closure
of the gauge algebra in the general case are discussed.
